From the perspective of the police force, prostitution being illegal is 1% moral uptightness, and 99% pragmatism. Having prostitution be a misdemeanor helps catch people in the act of other, more serious crimes, as the "crime" of prostitution justifies search warrants to otherwise-unassailable places. It's a workaround for a permissions issue, basically, and has no ethical justification.
>It's a workaround for a permissions issue, basically, and has no ethical justification.
I think you mean no ethical justification that you agree with.
For example, take as an axiom "sex should only be allowed between partners in long term monandrous relationships" and it follows logically from there.
This is an ethical justification. You just apparently disagree with the premise. Most theistic ethical systems have something akin to this as a rule (whether derived or axiomatic within the system).
I've only dabbled in moral philosophy (the study of ethics!) but my understanding is that the more common use amongst professional philosophers is that ethics relates to a system established usually by a particular group, like a legal code or religious doctrine whilst morals concern an individuals actions. Morality then is considered to concern a naturally occurring right whilst ethics concerns a constructed set of rules (often based on or intended to enforce particular morals).
Don't those other serious crimes generally stem from prohibition too? If you're running girls you might as well sell drugs too. Illegal gambling? Now you need guns to protect yourself because you can't call the police and report that your prostitute just stole $20k worth of cocaine from you. It's such a vicious cycle.
From what a policeman friend of mine told me, the busts they spend all their time on have the reverse of that story: a local gang/mob forms, and then, since they're already assaulting and murdering to keep their place in the criminal underbelly of the city, and since they know their shit well enough to be getting away with it, they can run as many side-businesses as they like doing other, lesser illegal deeds, because they've already ensured their protection. This is pride before a fall, because these lesser crimes—especially if they involve non-group others, like prostitutes or drug mules—can be the cracks in the dam that allow the police to nab them.