No, Ten, you're being very helpful.
My primary RP characters (as opposed to NPCs, supporting characters, etc.) tend to be young (or at least young-looking), white women. The young women thing doesn't really bother me (the white thing does, a little, but not too much). They definitely don't come from similar social backgrounds.
Their personalities are varied, but they tend to be idealistic, passionate individuals, and a lot of the variation comes in what they specifically care about, and how they've tempered or adapted to their own personalities. They usually have pretty complex internal issues and do a lot of introspection. Emily is definitely an example, albeit a darker one - her issues are relatively literal and obvious, compared to some of the others, but she's still part of the spectrum.
It'd be fine and good to write an old, black man instead of a young, white woman, and it would bring a new perspective - but I think I would still end up writing an passionate, idealistic person, even if the details were changed. I could make them ill or religious or whatever, but that doesn't really change the core; I feel like those traits, while interesting and useful to characterization, don't really change the central essence of the person.
What I'm interested in doing is not necessarily changing the surface stuff, because in my mind a lot of that flows from the core conception of "who the person is," but I want to expand my range from "idealistic passionate person who is deeply conflicted about X" to have more options. I'm just not really sure what else I'd find very interesting.