All you have to do is study the laws of prostitution elsewhere in the world to understand that they have little to no influence on sex trafficking. Prostitution is legal, explicit, and even taxed in the Netherlands, but sex trafficking remains such a major problem that some large cities, like Utrecht, have outlawed prostitution locally to combat the issue.
It may not end sex trafficking but legalising prostitution lowers harm levels on workers, but allowing them to seek medical care and police protection without risk of incarceration. There is no down-side to legalisation as many would say for drugs, as it allows problems to have legal solutions.
I'm not in disagreement with you about legalization of prostitution in general, but with regards specifically to sex trafficking, there is much evidence from several countries that legalization actually makes sex trafficking worse -- most likely due to increased demand for a service anyone can enjoy legally.
The issue comes up quite often in the local papers here in the Netherlands. Some other commenters here have pointed to some other reports from other countries.
All you have to do is study the laws of prostitution elsewhere in the world to understand that they have little to no influence on sex trafficking. Prostitution is legal, explicit, and even taxed in the Netherlands, but sex trafficking remains such a major problem that some large cities, like Utrecht, have outlawed prostitution locally to combat the issue.