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Prostitutes wouldn't be victimized by the gov't for selling what's theirs to sell. In fact, socialization could help to remove the stigmatization that many sex workers suffer as a result of lingering American puritanism, as they'd become government employees w/ benefits (no pun intended).
I think it is better to separate the given reasons in "because" premises.
It could potentially lower the amount of gun violence by providing thirsty young men with some much-needed release, and by being socialized, it removes the barrier of "wealth" from preventing any individual from fulfilling a biological imperative.
Paying for sex is already legal, you just have to film it.
There's no good reason it should be illegal without filming it.
Prostitution is unregulated, unregulated markets increase harm. Legalized and regulated prostitution would reduce harm.
It would reduce the sex slave and human trafficking market.
Prostitutes serve similar functions as psychologists. They have heard it all, and thus they can be told absolutely anything. Having a member of the opposite sex to thus discuss one's life struggles, as well as providing him or her with a level of sexual validation, can heal a stress-sickened mind.
Prostitution can have a negative psychological impact on people who prostitute.
It would allow people that can't typically have sex, to have sex.
Men wouldn't waste women's time with uncommitted relationships as much, since they could just buy sex.
People in general would waste others and their own time less if they could just buy sex.
People buy sex with gifts. There's no reason not to allow people to exchange money as well.
The vast majority of prostitutes are trafficed women forced into effective slavery of the worst kind. Legalising it because of a liberal middle class fantasy removes the protection of the law from those who most need it