I have glasses. None of the champions in league have glasses (except for sunglasses, which don't count).
I don't feel like lesser of a person because there is no fat-white-average-height-glasseswearing-nerd-champion in league. I can play league without a charakter showing who I am.
I have played mirrors edge and portal, and never have I felt like it was anything different.
The only reason why people feel like they need to identify with whatever they are playing to feel good is because they have been told that whatever they are doing/how they feel is wrong.
Having every sort of champion does not help.
This reminds me of the political party in my country that advertised themselves by having 50%male and 50%female people working for them. But doing that is sexism. It might look like it works towards equality, but it is the other way around. If you wanted to join them and work for them they wouldn't say no because you have no qualifications or whatever, they would say no because you were the wrong gender.
And what kind of champions would you wish for? A gay champion? Wouldn't that mean that now blacks and gays are worth making champions for, but transgenders were not good enough? Or not important enough? What if I identify as a bicycle, I don't think that they would ever implement a bicycle champion just because I identify as one. The only way to have this sorted out is to NOT THINK ABOUT whatever gender or sexual preference anything is.

I also don't think that women don't get into computer games because there are too little games they can identify with. I know gay guys that love playing computer games, but there is hardly any gay main charakter in any game.
This has way more to do with everything else but the fact that most main charakters in games are white males.