As has been pointed out by many posters, it isn't really a simple suggestion at all - it'd require a lot of resources to implement effectively. Furthermore, whenever businesses have sought to make things more 'accessible' there's inevitably demands for even more inclusivity. Instagram, for example, recently allowed people to pick from one of 41 different pronouns. It wasn't enough and Instagram was quickly accused of 'not being inclusive enough'.

I think that a line needs to be drawn somewhere, as I see it. I may be gay, for example, but that doesn't mean I need a gay character to be present in every game that I play. Even ones where I can create my own character.