That is one I think I've changed my mind on recently. I agree, in theory, with the idea that if somebody wants to sell sex that isn't the government's business. But we had a speaker at my law school last year that had worked for a women's shelter for 35 years, largely doing outreach to prostitutes that gave a pretty compelling counter argument. Her take is that prostitution is largely slavery. Not in some hippie dippie sense of treating women's bodies like property, but literal slavery. The vast majority of prostitutes started before they reached 15. The ran away from home and a predatory pimp found them, maybe they were even kidnapped or shipped here from another country where their family was threatened if they didn't comply. The pimp systematically gained control over them through violence, drugs, threats and manipulation to the point where they at least believe that they really have no choice.
So, the obvious response is that statutory rape and slavery are illegal, so we could just prosecute them for that without having to make prostitution illegal. But practically speaking that doesn't really work. A woman who is, for example, severely addicted to heroin and whose only source is her pimp, whose pimp has her kids while she's out, and whose pimp regularly beats her and her kids just is not realistically going to go to the police to report it and even if somebody else reports it, she isn't going to testify in court against him. Or, with statutory rape, it is much harder to prove. Police can't solicit statutory rape because the john is the perpetrator. Neither the john nor the victim are ever going to report it. Even if somebody does report it, that just allows the police to go after the john, it doesn't empower them to do anything to help the girl out of her situation. So, from a practical point of view, the only real way to fight it is to make the whole profession illegal.
I'm not 100% convinced, but that definitely gave me a lot to think about on the topic.