Some points about TSAB's policies.
First on the nepotism. I get the idea that they can't actually help it much. High level mages along the likes of Chrono and Lindy are
really rare, and on top of that, magical talents tend to run in families. I'm guessing for every 1000 or so D rank mages, there is about 10 C ranks, and 1 B rank, and A rank or higher mages are stupidly rare. This means that most of the high level mages are closely related to each other in some way. TSAB administers numerous worlds, but even with all those worlds, they don't have that many high level mages, and those high level mages are spread thin, and many haven't even joined TSAB, although they likely use a lot of methods to pressure them into doing so, because of their rarity. This including hefty benefits packages, luxurious lodging, top medical facilities, nice vacation time and special vacation facilities, and pressuring about the the whole Spider-Man thing, with great power comes great responsibility and all. They also likely have a lot of breaks in the law for mages willing to join TSAB to complete punishment duties, as skilled mages are hard to come across and train. Of course they have to pass duty training tests in order to qualify, which likely leave only the higher level mages able to avoid prison by working as contract mages for TSAB for a while...
Even people like Gil Gram(sp?), he is a powerful, high ranked, and experienced official, with generally the right intentions, if extreme and questionable ways of implementing his plan. Given he is powerful enough to support 2 powerful familiars, it would be very useful to re-activate him in an emergency situation. If his 'punishment' is more like a vacation, this means that he is more inclined to be highly willing to help out if they need to re-activate him. In the meantime, he is probably high ranked enough to understand these policies, and is making good with his victims so that they won't complain too much in such a case.
Regius doesn't have much excuses behind his actions, but again, he was unable to be punished given his death. His reasons seem to involve a number of complex personal issues including being pissed off that other branches are taking over his branch's duties, particularly in an issue that he is largely to blame for in the first place and was one of his own plots to power up his forces that backfired when Jail went rouge. On top of that, as someone who _doesn't_ get the high level mages who are typically investigators and air forces and stuff like that, but the lowest D-rank grunts of the ground forces, he probably likes a lot less the policies of lenience on criminals for joining the forces, thus is pissed off about the formal criminal stuff, and might not have full information on the circumstances depending on how far clearance levels go for those not involved in incidents, particularly ones that might be embarrassing to TSAB like Gil Gram's actions.
Children in combat goes back to the high level mages rarity bit, but might have additional aspects. For instance, it is highly possible, and likely, that mages mature much faster than muggles or whatever they call them in TSAB. They might even have higher intelligence, given Nanoha's mathematical skills and other hints we've seen. Additionally, it is possible for them to burn out their linker cores if they push themselves to much, and if they don't mature faster, it is highly possible that older mages tend to be a lot weaker, after pushing themselves too far numerous times. At least by joining TSAB they get training to better and more appropriately handle their powers, and better support if they get involved in incidents, unlike helpful civilians like Nanoha started out as. It is also possible, or even likely, that exceptions are made for those with talents in the class of Chrono, Nanoha, Fate, and Hayate, who are all massively powerful freaks of nature, allowing them to start active duty at ages below legal maturity on TSAB administered worlds if they pass a few tests, mostly geared towards high level mage geniuses to get them out on the field as quickly as possible... particularly since they're likely to get themselves involved anyway. Chrono is implied to be a rare genius who joined up and rose in the ranks at a shocking and unprecedented rate, and Nanoha, with her Starlight breaker blowing through armored walls and high class barriers with her Divine Breaker, is implied to be something like a case of breaking all the standards and barely still fitting within the capacities of their highest class measuring equipment 'What an insane amount of magical power!?' indeed, to the point they weren't sure Fate would be okay, despite all the spells being restricted into non-lethal mode. Hayate is so powerful they had to break out previously unused theoretical measurements of mage power to deal with her, even when she is sealed and powering the equivalent of 4 obscenely high class familiars around the same power range as Fate when Arf is powered down to puppy state. If she wasn't powering 4 familiars and sealed, she'd probably break their scale system and go up past SSS+ rank, forcing them to make a new scale.
On the seals restricting high level mages. It is true they need permission to break the seals, but it looks like to me that the permission is just so that they don't get in trouble when they do. They could likely turn them off on their own in an emergency situation, but would have to fill out numerous reports explaining their actions, and possibly be punished if their reasons weren't sufficient, or even just for going against orders, even if they were right to do so. It is in place to avoid large scale rebelliousness and negative feelings from the more average forces who aren't super-powered freaks of nature who get shamed just seeing the actions of high level mages, and forced into fits of jealousy and envy. If they didn't have this in place, they'd likely have a number of lower level mages constantly trying various power-up schemes or burning themselves out trying to keep up with the super-powered freaks, much like the path they had to deter Teana from when she was trying to keep up with her team-mates. Not to be sexist or anything, but it is likely that boys tend to be more competitive and push themselves harder than Teana did if they feel like they aren't contributing enough, so things like that are probably surprisingly common. I'm strongly tempted to call it the Sasuke effect after Sasuke in Naruto and how he goes to Orochimaru for power. Regius was trying to do similar for the ground forces in general by attempting to employ Jail to do combat cyborg research, which would allow lower class mages to function like high class mages using cybernetic enhancements, specifically because he was pissed off by the ego and power and area of interest conflicts he constantly had with the more powerful Air and Enforcer groups, in which his forces constantly appeared incompetent and had to get help from those groups, and the other two groups always got favored in equipment, benefits, leniency for forces who were previously criminal elements, and so on. If they didn't use the restrictive seals, the Regius issue would keep on repeating and be much more expected and common. In a sealed state, at least Nanoha's techniques can be replicated with enough training by similarly leveled mages, not that they can keep up with her anyway because she is still a combat genius using highly difficult techniques with ease with greater reflexes, tactical and strategic abilities than a Korean pro-Starcraft player. They use her as a teacher for a reason, not just because the forces she creates tend to be better, but because she has enough situational awareness and high class skills to maintain discipline in a group of high level mages who are used to overpowering their peers and using utility magic to make everything in life easy for them, as well as can consistently outsmart and out-predict them, so she can actually teach and keep in line lesser geniuses with bigger egos, earning their respect. They cultivate her 'White Devil' reputation on purpose, but still seal her power so what they generally see is actually attainable if you follow her training properly.
Most of TSAB's issues come from having to employ people who are far more powerful than most of their peers, and used to using that power to show off and get their way, and conflicts of interest between powerful individuals that are settled by force, when who is right and who is wrong factors in less compared to who is most powerful and talented. It is only pure luck that the people in charge are relatively good and have generally good intentions for the multiverse, trying to deal with multi-dimensional disturbances and sealing away of Lost Logia. They are, however, forced to take in as many high level mages as possible, as only the most powerful can actually deal with and seal lost logia properly. It doesn't matter how many ground forces you sent against the Book of Darkness, they'd all just die, and you wouldn't be able to do anything about it, but about 7 elite AA rank mages might be able to pull it off with the help of a top battlecruiser's main gun.
Notably, when Nanoha was first starting out, as shown in the cannon comics, she was doing mental training programs with Raging Heart virtually, in which she battled against whole platoons of A-B rank fliers, and was dealing with them with relative ease in these simulations. Increases in rank tend to indicate exponential increases in raw power, so it is hard to utilize ground forces level mages for what TSAB's main duties are. The ground forces are almost closer to a police force when it comes down to it, and only get their military status because they don't want to embarrass large numbers of people who are at least actually mages, and with the right training could still operate things like battlecruisers and high powered magical blasting guns that use something like a cartridge system power source to charge up over time, for a few key high powered shots, or cast group spells under pressure to try and make up for power differences, or worse, be tempted to try and make up power differences by using lost logia and other wisely forbidden techniques and technologies.
TSAB isn't similar to organizations in the real world because of this kind of stuff. Here in the real world there is little difference in the raw power and physical capability of our soldiers. There are those with physical disabilities of course, and even more noticeably those with different intelligence and skills, but this pales in comparison between different mage ranks, or mages to non-mages, which TSAB has to deal with. It would be like some kind of super-hero world effect, only a very rare few are super heroes, and amongst those people have vastly different power levels, so if you want to stand up against the biggest threats, you might be forced to work with or use the likes of the Hulk, the Sentry, or the Specter, or given that we are talking about anime here, it might be like being forced to work with ex-space-pirate Hakubi Ryoko, as one of the few able to stand up against the kind of threats they are dealing with at the time, or perhaps having to work with Lina Inverse, the Bandit Slayer and Enemy of All Who Live, although I don't think TSAB would go quite so far as working with someone like Dark Schneider.
As you see with StrikerS' finale, Nanoha, Fate, Hayate and other super mages tend to be the only ones able to actually do things, while the rest play support by taking out what AMF enhanced automatons they can, this means TSAB has to bend over backwards to be able to employ them.
As far as the 'prejudiced to non-mid-childeans' bit goes. Well, I don't think it is that, so much as their forces are _very_ stretched out already, they can't _afford_ to deal with every incident in some random non-administered world. They didn't even know the jewel seeds were lost logia until they found out after arriving to investigate the ship's disappearance, and Earth is far enough away dimensionally that it takes them a while to get ships there and back, and one ship was deemed sufficient for the incident.
With the A's season incident, the ship was already visiting Earth for reasons connected to Nanoha, they couldn't just have them sent back home and replace them quickly just because of a conflict of interest, especially when a conflict of interest might also mean the parties involved have more critical experience and knowledge regarding what they are dealing with. Gil wasn't even directly involved so much himself, but more available in an advisory role, at least officially, it was only later discovered he'd already had a plot in the background, which he likely kept secret because it broke numerous moral rules and regulations on dealing with citizens of non-administered worlds and children, and standard practices for how to deal with Lost Logia, as well as his desire to keep the site of it being sealed secret so that nobody would seek it out for power. They also happened to have some of the most powerful around, to deal with one of the most powerful and dangerous lost logia TSAB had ever dealt with. It's not like they could just pull out some other mages around Lindy and Chrono's level to help deal with the Book of Darkness and it's projected guardians. Also, who is to say that other capital ship crews wouldn't have numerous members with personal links, given crew shuffling and the fact that before Hayate, the guardians tended to drain mages to death to fill up the book, and TSAB had encountered it before, and developed beliefs that the guardians were emotionless AI's.
"Health, Learning & Virtue will ensure your happiness; they will give you a quiet conscience, private esteem & public honor." Thomas Jefferson (1743 - 1826)