Still, I'm not sure what you're describing is totally stringent in keeping with what a Mary Sue really is. You can have characters with sue-ish traits or tendencies, but that doesn't make them one.
This. You could argue Superman is a Mary Sue because this and this and that thing, for example, but he's not usually called out as one because he's missing a bunch of other criteria.
For that matter, main (and competent) characters in general tend to overlap with Mary Sues as far as being good at succeeding, seldom meaningfully failing, and having the story revolve around them. But without pushing those factors
all the way and tacking a few more on, that's not enough to mark them as Sues. And conversely, of course, not everyone labeled a Sue is the main character, because there are ways to be obnoxiously perfect and important without being the literal titular character.
In the case of Akagi, for instance:
BUT it works with Akagi because his opponents are not only larger then life, a lot of the time, but also the world is a bit more realistic so to speak so even though Akagi is a Mary Sue he still actually has to overcome disadvantages or just flat out luck against him.
The first bit sounds like he's high powered rather than Suelike, since his awesome amazingness is countered by similar foes, and the latter part makes it sound like he sometimes fails and suffers setbacks and so on. Both of those are typically major points in a Sue- that they face no
real opposition or challenge at any time, or when they do it's done completely awfully.