We sortof have prostitution right now, its just not blatant. Plenty of people's relationships are centered solely around money. (Why some women get referred to as 'golddiggers'?). The only main difference is that now, women date rich guys because they know the man has money, and will buy her lots of shit, and in general make sure she is happy and taken care of. Implied in the deal, of course, is that the rich guy will get to have sex with said woman.
The only difference (to me) between this and prostitution, is that prostitution is a *direct* deal, with a set price layed down beforehand. The couple puts a price on the sexual encounter and pays for it outright, and that's it, unlike the former.