"...prostitution would be acceptable!"

In some places, it is. (Holland, for example)(at least, the last I heard)

Prostitution, like homosexuality, is a problem when people do stupid things while indulging, and these are what get the headlines. I indulge in neither, but life has been such that I never had the need or desire. BOTH have a long history in human societies...(ancient Greece, etc.)

I'm afraid, ake, that you are unlikely to convince many that your main concern is really health. You may BE quite concerned about health, but it always feels as though you began with strong moral and social objections and have resorted to health concerns to justify them. That is the kind of attitude that is not always even obvious to those holding it. Can I state this with absolute certainty? Of course not.
All I can do is attempt to show counter-examples to some of your claims and recognize that human rights should apply even when many don't **like** who is getting them.