Even if prostitution was legal very few would go along with it.
Imagine going to a hooker in the Soviet States of America, where every meeting is registered including the transaction, and then someone finds you troublesome and you're arrested for retconned rape and it's on the news worldwide.
If it's not forced on anyone than I believe it is. With legal prostitution you (most likely) have less rape and way less illegal women trafficking. In Poland all the hookers I met so far were really happy with their "jobs"
Now child prostitution... different thing all together.
Not to mention it is much safer for all parties involved. No need to try and get skeevy/unstable men/women into bed and you can ensure that you have medical to deal with any issues that may arise. Amsterdam does this, IIRC with their Red Light District.
Obviously this is only relating to consensual adult prostitution. Anything related to children needs to be dealt with immediately and put to swift and abrupt end.