The reason is that prostitution produces those same problems on steroids.
Source?
No, you absolutely did not. You cited Supreme Court cases that struck down specific laws with that ostensible purpose, but which were ruled that way because of unrelated reasons, and you've decided to unhelpfully cite them as general "anti-government-infidelity laws" because you don't understand them beyond "these laws are unconstitutional".
Regulating infidelity is unconstitutional. You don't need to take my citations word for it. Feel free to look it up.
Those cases ruled that the laws violated privacy protections implied by the constitution, nothing to do with promoting marriage and preventing STDs per se.
You mean like privacy required for "infidelity"?? That's like saying that "regulating" anal sex is constitutional, because it was ruled unconstitutional on the grounds of privacy issues.
For example, if you started up a "I will help you cheat on your wife and hide it" service, that could be shut down, as the law itself does not require violation of privacy.