My hunch remains that if you really freed children sexually and removed all their hang-ups and inhibitions, they would use the freedom mostly for prostitution.

I disagree for the most part. Being rich plays a much larger part in attracting women than it does little girls. Little girls don't really know what being rich is or what being a prostitute is. They can only judge on what's presented to them based on what little experience they have. They're not going to want to go off with some creepy older guy just because he has money. They're not going to want to have sex with random creeps because said creeps are willing to pay for it. This is what adult prostitutes do, but kids will not willingly do this, an adult has to force them.

That said, if someone they know and trust and like wants to have sex with them without pay, they probably can be talked into it. On a similar note, if the same sort of person offers a quid pro quo deal, they might take him up on it. I've heard from some girl lovers that their girl sees them as a sugar daddy of sorts. He's willing to buy some things for her and she sees him as an adult who's a source of money for things she might want. But it's no different than how she sees her own daddy. It doesn't make her a prostitute or him a john, because there's no sex involved and no sex even expected.

It's just expected that adults pay for kids and to some extent that men pay for women. So an adult male is expected to pay for a female child. But I don't go along with your prostitution premise. Child prostitutes are mostly going off of the financial needs of their parents and community (in impoverished countries) or they are the victims of sexual exploitation by pimps (in wealthier countries) with some overlap between the models in many cases. It has little to do with sexual freedom in most cases.