If this woman is young and good looking she might not be physically capable of answering that many messages. One would need to quit her job to do all that. It's just not possible.

I am surprised to hear women like to be passive. Girlfriends I have quite often contacted men themselves. I did that as well. I don't know too many passive women nowadays. I don't experience men having to take initiate in everything at all. I lived on two different continents. It's pretty equal on both continents, in my experience. Maybe it was the case 50 years ago. Or maybe in some regions. I don't see it neither in the US nor Europe.