Stop... no. Reduce.... maybe?
Generally there are 2 definitions of trafficking, and each side of the debate generally uses one or the other, whichever fits their view.
The anti-legalization side uses the data that "trafficking" increases in countries with legal prostitution. HOWEVER.... they use the definition of trafficking that includes willing participants who pay someone to smuggle them into the country... it would be like calling half the migrant workers in the US trafficking victims. It's just illegal immigration by persons who then work as prostitutes.
The opposite definition is those who are unwilling, or otherwise forced, there doesn't appear to be any evidence that legal or decriminalized prostitution nations see more of this type of trafficking.
This does a decent job outlining the differences:
https://www.forbes.com/sites/timworstall/2013/06/15/legal-prostitution-and-sex-trafficking-from-the-annals-of-bad-economic-research/#10f1c7e95727
This is correct. Nobody is saying that legalizing prostitution will result in the wholesale eradication of human trafficking for sexual purposes. That's absurd, and it would be absurd if we tried to base our policy decisions on a success rate of 100% or nothing.
It's a simple supply/demand argument. I know there are a few folks around here who like to partake in the experience of smoking weed. For those of you that live in Massachusetts, how many of you are now driving down to the inner city, rolling down your window and trying to score some joints? How many of you are even buying it illegally at all? To those that are, I would say what the fuck is wrong with you? You can walk into a legalized establishment with an epic menu of every type of strain imaginable, take your pick and walk out the door without even worrying about a cop invading your space.
If prostitution were legalized, it would become monetized and regulated like any other industry. So at that point, why would you go to the seedy massage parlor where the women don't speak your language, may or may not be there of their own free will and you run the risk of being arrested, versus walking into a legal establishment that the government is regulating and overseeing, that probably provides a healthy variety of excellent choices, a nice night and no fears of ending up in prison or with your name in the papers?
If folks stop visiting these seedy places, and there is no longer a financial incentive for the "owners" to traffic these girls/women into the country, it would follow that more than a few would go out of business. And putting 1 trafficker out of business is probably better than none, IMO.
I would imagine Nevada would be an interesting case study. According to the Wiki, there are currently 21 legal brothels in the state. Is there a large sex trafficking industry in and around those areas? I would tend to doubt it, but who knows. But if there were 210 legal brothels in the state or 2,100 of them, I can't imagine it wouldn't result in a decline in women who were being forced to do it against their own will, just because of the sheer number of customers they are going to lose to the women who are tested, clean, working in regulated places and you know, actually want to be there.