And yet, a whole lot of men don't like that because it goes against gender lanes and then she's being too assertive, and that's not feminine... blah, blah, blah. And those beliefs are most likely taking place subconsciously, so he's not even aware that he's having that train of thought. He may even believe that he wants a woman who is more bold and then feel put off when he encounters one.

Plus, what you've described is her taking all the risks. "Here's my number. We should go out" which leaves the man with nothing to do but follow up. What I'd really like to see instead is men learning to read body language, and other cues that indicate interest, and ALSO it being broadly socially acceptable for anyone to ask anyone else out without gender roles being a factor.