More like individuals should be empowered by the law to charge money in exchange for sex. That's the thesis, the whole thing. "Party X paid Party Y for sex" becomes not a crime.

> do you really believe that human trafficking exists because child prostitution is illegal? And that such a move would actually decrease the number of, say, young girls are forced into prostitution against their wills?

It doesn't matter, it's unrelated to the central thesis. It's possible to agree people should be free to charge for or pay for sex, while also condemning human trafficking and other forceful restrictions of personal agency more generally.

They did not say all prostitution is consensual (and certainly not all trafficking, since that's pretty much defined not to be consensual). And they said absolutely nothing about child prostitution.