Ceteris paribus (though remember there's a long and ugly history of the police victimizing sex workers as well).

But all things aren't equal. Most importantly: so long as prostitution is formally illegal, men and women can't be pressured by social norms to participate in sex work. Once prostitution is legalized, the stage is set for that to change: perhaps body integrity isn't nearly as important as bootstrapping oneself to self-reliance, or providing for vulnerable family members.

Usually in economic analyses we stop and ask ourselves if normal people would prefer the choice rather than having it foisted on them: for instance, maybe we'd rather allow ticket scalping because someone with a valuable ticket would probably prefer the option of being able to sell it for a steep profit and pay for health care rather than just having the experience promised by the ticket. But here we have a case where most normal people probably do not want the choice deregulation would allow.

>though remember there's a long and ugly history of the police victimizing sex workers as well

Mainly in areas where prostitution is illegal, thus the police use their power over the "criminal" to abuse them.

Sex workers have no legal method to report this abuse with out also admitting to a crime themselves.

Thus if it were legal, Abuse by police would only be as frequent for sex workers as is for other legal occupations, which much hire than it should be but....

You do know there are western countries where prostitution is legalized, right? The moral and social fabrics of these nations are not unraveling at the seams.

> Most importantly: so long as prostitution is formally illegal, men and women can't be pressured by social norms to participate in sex work.

Untrue, social norms can pressure people into formally illegal acts quite easily, and that absolutely happens with sex work now.