The job market paper of Amanda Nguyen, of UCLA, is on that topic, I found her results intriguing:

Despite its illegality, prostitution is a multi-billion dollar industry in the U.S. A growing share of this black market operates covertly behind massage parlor fronts. This paper examines how changes to licensing in the legal market for massage parlors can impact the total size and risk composition of the black market for prostitution, which operates either illegally through escorts or quasi-legally in massage parlors. These changes in market structure and risk consequently determine the net impact of prostitution on sexually transmitted diseases (STDs) and sexual violence. I track the impact of two policy changes in California that resulted in large variation in barriers to entry via massage licensing fees. Using a novel dataset scraped from Internet review websites, I find that lower barriers to entry for massage parlors makes the black market for prostitution larger, but also less risky. This is due to illegal prostitution buyers and suppliers switching to the quasi-legal sector, as well as quasi-legal sex workers facing a reduced wage premium for high-risk behavior. Consequently, the incidence of gonorrhea and rape falls in the general population. I also present evidence that growth in the quasi-legal sector imposes a negative competition externality on purely legal massage firms.

I don’t find the rape result intuitive, but I am seeing it pop up in a number of papers, so perhaps it should be taken seriously.