Your theory is that, let's say, John Carmack can't self-identify as a genius after all he has accomplished, and given how far out in front of most others he has always been on the technology curve?

Bill Gates possesses a genius level intelligence, has the accomplishments and mental demonstrations to back it up, and is apparently fully aware of it. What's the problem exactly?

Let's define genius:

"exceptional intellectual or creative power or other natural ability."

or

"a person who is exceptionally intelligent or creative, either generally or in some particular respect."

As though it should be difficult for a genius to recognize that their abilities far exceed those of other people.

I would argue that being oblivious to that level of blatant genius - having no idea you're so much better than most others - would be more of a negative mental trait vs being aware of it. You'd have to be incredibly ignorant, and almost entirely non-self-aware to miss such a thing across a lifetime.

If you can reasonably be defined as to be in possession of X trait, there is absolutely nothing wrong with recognizing that. It is not an ego problem to do so. If my brain is capable of great feats of mathematics, and I can tell that I'm drastically better at math than my peers, there is nothing irrationally egotistical about recognizing it. With there being a critical distinction between recognizing your capabilities, vs. obnoxiously promoting them to others.