I would agree with most of this... yes in the end it's the woman's choice. She may have a reason, she may not have a reason, or she may not know the reason.
A couple of other things: we men do look for more than just looks; I actually have a thing for the sound of somebody's voice. I love accents. The woman I am with now...she is incredibly empathetic. A woman who is genuinely nice, will get a lot more of my attention. And a woman who is preening her looks for maximum attention, I will usually ignore.
I will agree with comments, women these days are much more assertive in approaching men than they were 10-20 years ago. But they will still want men to take the lead in some aspects - and early. At least be able to plan a damn date. Make it memorable. Once you connect, you can then figure out who will take the lead on what.