You can make the argument that what two consenting adults do in private is THEIR business, and I'd be willing to entertain such a view if this was actually done in private. But it generally isn't. Oh sure, the actual act usually is, but the solicitation is decidedly public, at least on the few occasions when I've actually noticed such activity. So, come up with a way to keep it out of sight, and I'm prepared to leave each to their own.
It seems likely to me that the main reason for that sort of solicitation is that there's no way for a legitimate business to advertise. You can't set up an office or a store. You can't put an ad in the paper and stay at a fixed location. You need to move around and proposition people who seem like they're not likely to be cops. I don't think any legitimate business would advertise that way, given the choice. It's not like dentists or hairdressers solicit in the streets.
However, the problem with this "activity" is that it encourages things like human trafficking, which is far from a victimless crime.
This seems again to be primarily a problem with it being a criminal activity to begin with. People don't get trafficked and sold into slavery as office workers. So what is it specifically about prostitution that makes it special? I'd say it's primarily because it's an illegal profession and people who go into it have two choices: 1) Do it alone and hope you don't get murdered by a client or by the organized criminal who stakes a claim to your territory. 2) Join up with a pimp who is an organized criminal and very likely a dangerous sociopath. Blaming prostitution for human trafficking of prostitutes is a little bit like blaming drugs for drug smuggling drive by shootings. Those things are a natural consequence of a profitable business being completely run by criminals without any oversight.
Remember, we've had quasi legal prostitution (still do in some places) in the past where the police colluded with brothel operators and it didn't work out all that great for the average worker, but made boatloads of cash for the owners. Consider Chicago in the 1920's, I don't think we want to do that again.
Can you flesh this out a bit? Are the problems of Chicago in the 20s still something we observe today in, say, Nevada? Without knowing more details, this still sounds like a problem with having entrenched organized criminals running an industry.