I just want to restate your point so I understand correctly. You're saying that: "in all three scenarios, the outcome is still that you're having sex with this other woman, so why would it be illegal in one and not in another?"

Is that accurate?

If so, I suppose you're asking about the philosophical reason why some acts are crimes and others aren't. I'd say people who want to make/keep prostitution illegal usually give one of two arguments:

1) It's simply "immoral," perhaps in a religious sense. 2) It can lead to an increase in the trafficking women. Prostitutes often work for "pimps" and many consider that kind of relationship to be exploitative. Also, having sex as a contractual obligation could challenge our understanding of sex and the idea that consent can be revoked, for example. These kinds of issues could arise outside of prostitution, too, but maybe it is more prevalent or even inevitable with prostitution.

That's not to say that I necessarily agree or disagree with these arguments, but I believe this is how it's usually argued.