Hey, call me old-fashioned but I still believe there are much bigger differences between male and female than just what is obvious to the eye.
You don't even know what kind of ball you'd be rolling. Read the Bible. God's plan for husband and wife is spelled out in it. First of all the husband is to be the head of the wife, a strong leader and provider. If he's too afraid to ask a woman out in the first place, what makes you think he can step up and be a man in other areas of life? What makes you think he can lead a wife effectively with all that fear in his way? Second, the wife is to be submissive. She's not meant to take control in a man-woman relationship. If she can't even wait and trust her future husband (whoever he is) to initiate their relationship, how can she be expected to trust him and let him lead in other areas of life without interfering?
Here's a simpler way of putting it: A man's #1 need is to be respected. A woman's #1 need is to be loved and desired. When a woman has to ask a man out, his need for respect isn't met because she didn't let him initiate the relationship, and the woman's need to be loved and desired isn't met because he didn't desire her enough to overcome whatever shyness and fear he has to ask her out.
Oh and I'm not sure if you knew this, so I'll share it. In the garden of Eden it was Eve who initiated the eating of the forbidden fruit to Adam. She certainly got THAT ball rolling.. So when God punished her He said "your desire will be for your husband, and he shall rule over you". But do you know what that means? It means that in every man-woman relationship, the woman's desire will be to control or posess the man to some degree. (When translated, the word "desire" in the Bible often means "desire to control", especially in reference to Satan's desire for us, God's people. But it is also used in Genesis to describe the woman's punishment for manipulating the man.. She will forever desire him.) But nevertheless God says that the man will rule over her. So whenever a woman tries to turn things around, tries to push or nudge or otherwise MANIPULATE the man in her life (or the man she wants to have in her life), the outcome will never be good for her. Your best bet is to tame the urge to control. You will still experience some nagging desire to take charge, but it will be far better than acting impulsively and screwing things up.