Abhorsen was arguing that legalizing prostitution would put the genie back in the bottle and traffickers would magically disappear when that prohibition ended, and claimed Al Capone was proof of it.
No, Al Capone was specifically cited as an example to show that prohibition doesn't stop X, and have bad side effects. Just removing the banning doesn't put the genie back in the bottle, but it does allow progress to actually be made. With or without prohibition, there will always be a market for X. If X can be provided in a moral, consensual manner, and isn't a threat to others (not including the user), banning it is worse than letting it be, as it finances organized crime, and if lucrative enough, will result in gangs by itself. Even if we won the war on drugs tomorrow, and all illegal drugs and drug dealers and narco criminals et al were gone, in a few years it would be back because it is that profitable. The only way to make any headway is to legalize this.
This is less true for prostitution, as much of it can't be made legal (child sex is inherently non-consensual), and it's not as profitable as the drug trade, so usually sex trafficking is attached to other gangs instead of being the primary income earner.
Given that you have repeatedly shown a tenuous connection with it, I hesitate to look further. But I did, and the post was remarkable short on statistics, but very long on talk. So shockingly, having one place in Europe known for legal brothels obviously means that all the sex slavers will head there, and there was clearly no enforcement of the law trying to rout out illegal sex trade. This doesn't mean there was an increase in sex slavery in Europe, just that the sex slavery all was attracted to Amsterdam. There's also legal slavery in many other places in the world without horrible oppression, such as Australia.
They have been caught by activists. There is an ex-employee flat out saying that they're taught to evade the law when it comes to things like this.
Again, I warned about exactly this kind of proof. All you have shown is employees willing to do bad things. Also, you haven't even established that these employees do these things, just that they would if given the chance.
But, legalizing prostitution as what Abhorsen were saying have been refuted. He claimed things that has a different result in real life.
Fleiur: you haven't actually refuted anything, other than your ability to apply economics well. There are other things that would help, but there will always be a market. If it's illegal, that market will be an uglier one.