They shouldn't HAVE to, but an upscale college woman should be able to take a few jobs on the side if she wants in lieu of a full-time job.
Maybe someone is a sex-therapist who's wanting to experiment with actual sex in the context of doctor/patient/couples therapy well, they're getting paid so is that prostitution if she shows the wife different techniques or something?
Should the hypothetical homeless woman who's already suffering -- be put in jail -- giving her a felony so she's now even LESS employable?
Just locking up our "problems" doesn't fix anything. It didn't fix anything with drugs it won't with sex. It just creates black markets which are tax-free and have no legislation.
If you at least legalize it, require a business license, sales tax, and STD tests you kill some major problems in society like STD spread, you give the sex-worker more confidence to maybe move to a different career because now she's "legit" and not a "criminal".... etc...
In the specific case you mention making it illegal doesn’t remove the underlying economic imperative. It just punishes the women for being poor and needing the money.
More generally it takes away the liberty of other people (men or women) to do what they want with their own bodies to (not successfully) protect a particular group.
I mean nobody should have to sell sex to survive certainly, but if I was going to be homeless otherwise I personally would rather the option at least be legal if I were to choose to take it.
I can see no mechanism by which legalising sex work wouldn't force anyone to go into it, anymore than people might be forced to go into it by circumstances already. If you can think of one I'm willing to hear out this line of argument, but otherwise I think the fact that nobody should be forced to do it has nothing to do with the question as whether or not choosing to do it should be illegal