First of all... snip
Your first point:
While they may be aware of the problems with inbreeding and the Kiss of Marriage does insure that whoever joins the Amazons (willingly or not) are strong, but it also does a major thing to to enhance that problem: It severely limits the number of people that can join the tribe through marriage.
As isolated as the Amazons are supposedly are, they would have very few outsiders coming to their village and even fewer of those outsiders that can defeat a well-trained amazon martial artist - unless it is by accident like Ranma did.
Let's break this down:
First, let's be generous and say over the course of one hundred years the Amazons see about one hundred outsiders passing through their village; outsiders being defined as people totally new to the area. Second, we will be generous again and say seventy percent of those outsiders are male so that means that the village sees seventy outsider males. Let's further be generous and say that one in ten of those outsiders has any martial art skill of merit, that leave seven potential mates. Now, we will extend that generosity to say that one one out of ten of that remaining seven are skilled enough to challenged and defeat a trained Amazon for her hand.
This would mean about once every one hundred thirty to one hundred forty years an outsider would able to marry into the Amazons; or about twenty two to twenty three men over the course of the entire three thousand years of Amazonian history. This is not enough of a genetic diversity introduced to belay inbreeding.
However, I do agree that there must be other factors involved in the dispensing of their marriage laws or the Amazons and the Musk would have assimilated into one peoples by the time the Soatomes crossed their path. From what I've seen the in the manga, a Musk is more than a match for an Amazon warrior and if they follow their marriage laws to the letter, the Amazons would be no more.
Since this didn't happen, some other factors must had come into play. There is no doubt other villages (other villages are mentioned in the manga - just not what relationship they have to the Amazons) must be involved, but how those mates are judged, selected and paired up is up to great conjecture.
So on that, we can retire this argument of Amazonian genetics due to lack of evidence one way or another.
Your second point:
You proposed the possibility of Ranma staying in Japan after he married Shampoo (or in the case of the manga, recognized the marriage). However this is contradicted by the manga where there is little doubt that Cologne and Shampoo would insist that Ranma return with them to China and they have stated that fact several times throughout the series. It would be highly unlikely that the Amazons would allow Ranma to remain behind, even if Shampoo stayed with him, because Ranma cannot benefit the village if he stayed in Japan.
The scenario you proposed, as interesting as it is (and maybe a good fanfic could come out of it), does not fit the events laid out in canon and therefore irrelevant to this argument.
The problem that you seem to be missing and that I tried to stress in my last posting is: In an arranged marriage, the agreement generally must be mutually beneficial for both families. Mutually beneficial - as in it is: Good for both participants.
In light of that definition, there is absolutely no benefit to the Saotomes in an arrangement between Ranma and Shampoo. None. Zip. Na-dah. Zilch.
In fact, it would deal the Soatomes a great blow. They would loose their only son, heir, and everything that they invested into their him and their future as well. It doesn't make sense from the Soatomes point of view to accept such a disadvantaged agreement.
Since you seem to have the most problems dealing with the fact that the Amazons are not the most with the benefits and instead are the ones with the least, I'll lay it out for you:
Amazons: Let Ranma and Shampoo marry! If you do we will teach Ranma all of our ancient and powerful martial arts techniques! He'll become a martial arts god... or goddess... depending on the water temperature!
Soatomes: Okay, that sounds good. It would benefit him and our martial arts, but what about the long-term benefits? What would they be?
Amazons: Isn't it enough that he be taught three thousand years of Amazon martial arts?
Soatomes: No, not really. You see, it is our custom that the children look after us in our old age. How will our son support us when we get too old to work?
Amazons: Well... you could come back with us to China. We can arrange something there.
Soatomes: Wait, wait, wait. You mean to tell us that you want our son to leave Japan and live with you in China?
Amazons: Yes, of course. Where else would they live?
Soatomes: Why here, of course. That way they can try and find a place to teach martial arts and start making a living.
Amazons: Impossible. How can Shampoo and Ranma benefit the tribe if they stay here?
Soatomes: How can we benefit by having our only son marry Shampoo and made to live in a foreign country, far from where we are, with no visible means of supporting us in our old age?
Amazons: Er... like I said, you could come with us.
Soatomes: To live in a foreign land? In a village that is more or less isolated from the rest of the world? Live amongst and having to embrace a foreign culture and laws? Away from our country, people and the life we know? All for YOUR advantage?
Amazons: Er...
Soatomes: Why should we agree to this when there are others interested in our son that won't insist that we uproot ourselves and adapt to your lifestyle?
Amazons: Er... let me get back to you on that.
See? Having martial arts as the main benefit doesn't work unless it can be backed by something else; something that the Soatome family can gain from in the long-term. In the manga, the Amazons don't have much else to offer beyond isolation and martial arts and thought I wrote the above very tongue-in-cheek it does show the some of the core issues involved.
Bottom line: While on the surface the Amazon martial arts may look like a good deal, without something more - in the way of long-term benefits for the Soatomes - it really isn't as great a deal as you think it is. Ranma can learn all the Amazonian martial arts they have, but without any real means of transferring that knowledge into something tangible - like income - it is meaningless to the Soatome family or their retirement. Once back among the Amazons, I cannot see how Ranma would be able to profit from this knowledge; while he would be a boon for the Amazons because they have acquired an excellent fighter to help defend themselves and to train future fighters.
With no compelling counter-argument to mine (your stance is mainly based on a "what if" scenario and nothing from the manga), my conclusion of "there would be no benefit to be gained in an arrangement with the Amazons" stands.
Third point:
As far as how much Akane has improved, read the first and last few volumes of the manga. Akane has definitely improved over the course of the manga while, in comparison, Shampoo has pretty much remained stagnate or improved very little.
Since canon supports this, it stands.
Your fourth point:
The Tendo dojo having no students is leans more toward fandom - what is known is that Soun does support the household somehow and the most logical way for him to do so would be to run the dojo. As I stated in my last posting, this is not supported directly by the manga, but Soun making some type of income is - the evidence being that he mentions going on business trips. However this being tied in with the dojo is all circumstantial, but it is not outside the realm of possibility or probability.
The problem with your argument is that you are trying to prove a negative. Any scientist and lawyer will tell you that it is impossible - you cannot rule out any possibility until the correct one is proven or concrete evidence is offered. The best that you can hope for is to propose a line of argument that says "There is a high probability that the Tendos have no students" but the fact is that "probability" is in there leaves the chance of them having students in the equation.
The only way you - or anyone else for that matter - can prove that the Tendos have no students is to find the definitive proof - the smoking gun. You need to find where in the manga that shows one of the Tendos saying "We have no students". That is the only way you can win this argument. Anything else is a guess on your part and given what I have read, your guesses are based on evidence that is more nonexistent than my argument that the possibility exists.
So basically, we have two theories here. The positive one that can be somewhat supported by highly circumstantial evidence and conjecture and the other, negative theory, that is not really supported by anything.
Seeing that my theory makes the most sense of the two, my educated guess that the "possibility that the dojo is still functioning on some level with the added possibility of some students" stands - but only marginally because for all we know Rumiko Takahashi, the creator of Ranma 1/2, might have intended for Soun to work a gigolo or something.
Your final points:
This really killed me:
First of all, Ranma has not been taught to teach- he has been brought up as a powerful martial artist, but it seems to me that Genma was intending for Soun's daughter to do the actual teaching and Ranma would defend the dojo and know the powerful techniques.
That made me shake my head in wonder...
In the manga, there was no provision for any of Soun's daughters to teach. There isn't any provision for any of the daughters to even KNOW martial arts.
Though the term "joining of the schools" is widely used, this is doubtful the only intent and fairly obvious that it extends to joining the families.
Concider: If there was a intent to "join the schools" then Akane, as well as her other sisters, would have been trained more rigorously to filled their future role - or, alternatively, one would have been selected as the official heir and trained and would have been automatically assigned as Ranma's fiancée from the very beginning.
But that is not how it played out in the manga.
Instead, Ranma was given the choice of "picking one" among the Tendo sisters to be his bride.
Pay attention! This is a very important plot point! Why? Because to shows in canon that knowing martial arts or knowing how to teach martial arts on the part of the Tendos sisters had absolutely NOTHING to do with and was not a factor in the decision on who was going to be Ranma's wife. It wasn't even brought up by Genma or Soun - who arranged the marriage in the first place!
Reread the above again just incase you missed it.
Ranma's decision as to whom he was to marry was taken away from him by combined efforts of Nabiki and Kasumi, but the fact remains that knowing martial arts was not a determining factor in what would have been Ranma's decision. This also demonstrates that, as far as the Soatomes and Tendos are concerned, "joining of the schools" means the same thing as joining the families.
If Ranma were quicker, he might have picked Kasumi or Nabiki, two people with no real martial arts experience, and Soun and Genma would have been just as happy and fine with that decision. Conclusion: Based on the events of the manga, passing on Tendo's School of Martial Arts was not and is not a factor in the Soatome/Tendo agreement.
A good example in canon of how irreverent martial arts was in the agreement on the Tendo side was the time that Nabiki was engaged to Ranma. The fathers didn't care as long as it was a Tendo and Nabiki didn't sell the dojo.
As far as Ranma teaching goes, before you can teach, you must learn. Ranma is still learning and it would probably be years before he is ready and has acquired the maturity to teach. Ranma not knowing how to teach is irrelevant at this point in his life and the assumption that Ranma's sole role is to defend the dojo from challengers is just simply absurd and laughable.
Akane's lack of control on her temper and Soun's broken, emotional state are based mostly on fandom and not canon. When arguing about canon, please keep your points solely to the canon. I'm not arguing fanon.
Your "strikes" at the end:
First: I have already successfully argued - as much as the scant evidence allows - that the probability exists that the Tendo's dojo is functioning on some level. Though I admit the evidence is highly circumstantial, it is far more than than exists to show it does not operate in any capacity at all. Soun's emotional state is more overly done in fanfiction than how he is shown in the manga (I do admit guilt in partaking in that - it is just so much fun to do!); he is far from the emotion wreck that is commonly portrayed. To clarify: Soun is a emotional man, but not an emotional wreak.
Second: As far as Ranma and Akane relationship goes, I can see them settling down - really I can. I'm forty-four years old and I've seen all kinds of relationships work out and what they have isn't too bad to begin with. The only problem I really see between Ranma and Akane is that their personalities are too much alike however, once they "wear some of the edges off each other" as I call it, they would most likely get along just fine.
On a personal note: In spite of Akane being the best match amongst Ranma's suitors, I will probably never write a Akane/Ranma matchup. I have my reasons and I won't detail them here.
Your "third strike" is based completely on a very early or fandom version of Akane's character and not how she is shown through the majority of the manga. Which is only relevant if one were to do a very early divergence fic.
It seems that your preference for Shampoo has caused you to overlook the way the situation is in the canon.
For arguments sake, let's say that Ranma has no commitments to any families and is free. No Kiss of Marriage, no pervious deals with the Tendos or Uyko - no nothing. Let us have the four interested parties visit the Soatomes to arrange a marriage agreement. This way we can look at the benefits and disadvantages on an even level. Please keep this in mind: For the Japanese, they decide such things based on what is best for the family, not the individual.
For briefness sake, I'll summarize though others could probably add onto what is here:
Ukyo:
Since running a resturant is not in the Soatomes plan, Ukyo has really nothing to offer them. Since martial arts are more of a side line for her (she trained herself) to the running of a restaurant, the Soatomes really don't have much to offer her in return - unless Ukyo wishes to expand further or go exclusively into martial arts. If that is the case, then the Soatomes have more to offer than Ukyo does and the only thing Ukyo has to offer would be a steady income from her business.
So this is more likely a lose/lose deal for both or, in the case of the latter proposal, a marginal gain on Ukyo's part and a marginal gain for the Soatomes.
Tendos:
They have an established dojo for Ranma to teach in when he is ready to do so. This dovetails with the Soatomes desire to keep their family art alive and pass it on, and the Tendos would acquire a teacher to carry on their dojo into the next generation.
This would be a comfortable win/win situation for both parties.
Amazons:
As noted extensively in my arguments: They have nothing beyond martial art techniques to offer and combined with their insistence that Ranma return to China with them makes the Amazons a poor choice for long-term benefits. The Amazons would have everything to gain (a husband, breeding stock, an excellent fighter for the tribe, etc.) and the Soatomes nothing.
However, depending on how realistically you want the situation to be, there can be other factors that would come into play that work against the Amazons. These are more "real world" issues that never showed up in the manga, so I discounted them for this argument.
The conclusion is that such an arrangement would be a huge gain for the Amazons and a huge loss for the Soatomes.
Kodachi:
If wealth with the probability of power that goes along with it are determining factors, then an arrangement with the Kunos would be a sure thing. They have sizable property and wealth and most likely political and social connections as well.
A big plus that the Kunos also have is a supposedly long Samurai heritage that would fit lovely into the Saotomes mindset and, in turn, enhance their social standing. Unless the Kunos are interested in enhancing their own family's martial arts with that of the Soatomes, the Soatomes have really nothing or much to offer them beyond that.
This would be a loss or slight gain on the part of the Kunos while the Soatomes would gain outrageously big time.
Final conclusions: An arrangement with the Kunos would benefit the Soatomes the most, followed by the Tendos, which would benefit both families. Ukyo has only a marginal offering and the Amazons have really nothing tangible in the long-term. In my opinion, these are what the benefits and losses would be from each of Ranma's suitors. As stated before, these conclusions are based on the traditional Japanese mindset toward marriage as applied to these characters and events.