Your point is contradicted by the fact that Germany, where prostitution is completely legal are the single biggest destination for human trafficking victims. Literally dozens of thousands of them.
Legalising brothels removes the social stigma from prostitute clients increasing demand for prostitution by the order of magnitude. Which gives human traffickers additional incentive.
I think that the good solution is what we have in Poland:
prostitution is legal for the clients and individual prostitutes but it is illegal for any third party (e.g. pimp) to interfere and make profit from prostitution. This gives a prostitute possibility to just go to the police and denounce her pimp, making it much harder to force her to sex work.
Building construction is a legal trade in Germany. There are a lot of illegal immigrants working on that trade too. Maybe the relation is more to do with the "booming" economy.
> Literally dozens of thousands of them.
Citation needed.
> increasing demand for prostitution by the order of magnitude
A whole magnitude? Citation really needed.
In Germany a john has to report to the police if he suspects the prostitute is being coerced, if there are legal women, why would he seek an illegal one and risk jail time?
I see the German situation more a sign for completely negligent authorities. Pimps are illegal in Germany too. Prostitution is only legal as a contract between the client and the prostitute. But all of this only matters, if authorities perform regular checks which they often skip.
Even if we accept what you say as true, it doesn't contradict the point. It is possible that even if trafficking to Germany increases, the global rate of trafficking decreases, which could be explained by a lot of people going to Germany instead of buying illegally locally. You show it concentrates the rate of buying and trafficking, but not that it increases on average. (I do understand that actually showing it increases on average would be extremely difficult given that it would require a continent level study.)
IMHO, the fact that Germany is surrounded by countries where prostitution is illegal is one of the causes of human trafficking victims. If legalization is generalized, this may reduce.
The problem with Germany is that Germany is now servicing not just Germany, but also its neighbours because it's an island of legalisation. As a result demand is higher than what the local workforce can provide, making human trafficking profitable. Also regulation is lax and mostly unenforced
Legalising brothels removes the social stigma from prostitute clients increasing demand for prostitution by the order of magnitude. Which gives human traffickers additional incentive.
I think that the good solution is what we have in Poland: prostitution is legal for the clients and individual prostitutes but it is illegal for any third party (e.g. pimp) to interfere and make profit from prostitution. This gives a prostitute possibility to just go to the police and denounce her pimp, making it much harder to force her to sex work.