I'd love it if girls asked guys out, but for the most part, they don't. Usually they give away hints, and get frustrated if a guy doesn't pick up on them.
In my view, no gender should have any expectations on the other. Women shouldn't expect men to conform to gender roles, and men shouldn't expect women to conform to them either.
Personally, I'd rather be single the rest of my life than be with a woman who had a very sexist idea of what she wanted out of me.