Because letting Mongo solve the issue is so morally correct, and just dumping a hooker's body in the river when she gets a little uppity is so fantastic to let happen.
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Society already has to handle the burden. We sit here and act like if we just ignore this little problem it will go away, stay hidden and not bother us in our cushioned lives. Fact is, every one of those beaten, broken women who feel like they have no where else to go could instead be empowered individuals if we just took a little time to take them from the fringe and give them a chance.
Literally every other society has, at one point or another, or even now, allowed Prostitution. Only America, foolish, Puritan America, doesn't except for one state that everyone agrees is fucked up. But then we wonder why people will go to such great lengths to satiate carnal desires.
Seriously, most people who attend strip clubs are older males, and I would assume the ones attending the brothels would be as well. sure, the urgency leaves, and your outlook does change. However, not everyone's outlook changes to the opinion that it is unnecessary. Some want it even more. Yes, young men will take advantage of it too, and so will middle aged men.
I've already dealt with your opinion of crime: force it into buildings, and arguments over payment won't happen. And if they do, well, that customer simply isn't going to be able to come back. It's exactly what happens when someone tries to steal from a restaurant.