Accepting who you are and overcoming obstacles is something that happens to literally everyone. It doesn't have to happen to someone "like you" to empathize with it. Don't you think that's a bit narcissistic?

I empathized and found solace in life is strange and Max is pretty clearly written to be a lesbian. I empathized with the lone traveler in Outer Wilds and I'm not an alien. Same thing for the relationship between Dante and Vergil in DmC (even though my sibling isn't a half-demon) and various characters in TLoU (frank, joel, henry, abby, ellie, etc).

Lastly, Master Chief isn't a "member" of any community (if 343 says he is, that's just because it's hip and it positively affects their bottom line, there's nothing on that topic in the actual games). That's just you projecting and his journey's success has nothing to with being queer, bi o heterosexual so I'm not sure how that's inspirational.

For some people having the characters be more relatable to them in personal traits helps them to put themselves in their shoes. For others it's not that important. Both are are perfectly valid ways of going about it.

One of those options is significantly more narrow-minded than the other.