I think it's advantageous to punters to book through the booking system. It allows the the SP aswell as yourself to leave fb. If you get good fb then it counts towards your +ratings; thus more girls willing to see you.
Well, do it that way if you like.
I am not interested in any girl that doesn't display a phone number. Why go to all the trouble of booking through AW? Just call the girl, have a little chat and, if you like the sound of her, make a booking. The advantage if this is obvious - you can get a pretty good impression of a girl's attitude during a short chat. Of course, sometimes you are talking to the madam, but even this can tell you quite a bit.
I have no presence on AW, but I have never been refused a booking over the phone. No phone number, no business from me. There's plenty out there who'll take your money, after all.