Maybe we should come up with a name that complements Mary Sue and spread it throughout the interwebs. That said, it should be a guy's name. Which would actually make sense, considering how often guys play stupid and incompetent characters, whether they're the protagonist or not.
I was browsing around for subjects on this, well, subject, and the closest thing I could find for this concept was
this trope. Though, if you read it, it says that it's the opposite of a Mary Sue. I don't believe it is, however, since the role for this trope in question is either still integral to the plot (especially if they're the protagonist) or meant to draw favorable attention from the audience (just not the wish-fulfillment variety).
What separates the concept in my head from that trope and the
Anti Sue trope, is that the plot/story can live without them. It would be like... An extra character that serves no real purpose plot-wise getting an inexplicable amount of exposure as if they were actually important somehow. They would basically be a waste of time in a serious plot, contributing or affecting nothing of significance, yet might not be too divorced from a joke character in a comedic context. Ultimately, as opposed to a Mary Sue, whose presence usually warps the plot so it can't live without them, this character will most likely inspire questions like: "what's the point of this character's existence," or, "why do I feel like I just lost time that I can never get back."