“Stamping out” anything moves it underground. The transaction volume almost always goes down and the risk for those remaining in the market almost always goes up.
Prostitution is called the oldest profession in the world for a reason. It has always existed, in all countries, cultures, etc.
IMHO legalized prostitution with some sane policies for health and safety combined with a threat of prosecution for 'customers' of victims of human trafficking (e.g. for rape, because that's what that is) would do wonders to clean that business up. A blanket ban just drives women in the hands of criminals.