Countries where prostitution is against the law have higher rates of prostitution than in countries where it's legal. Child prostitution will be no different. Taking away a major legal blockade in hiding a crime will make that crime occur more frequently.

Children are far easier to manipulate than adults. I'm not talking about forcing kids to sell themselves (though that would become more common as well) I'm talking about grooming children into prostitution. Making them accept it as something normal. It's trivial to groom prepubescent children for such things.

I don't care if you wouldn't pay for a child prostitute, but SOMEBODY will pay for it. And there will be more of those people if you make it easier for them.