That's not the only way you can get caught for prostitution. Suppose they have a search warrant. Sec 10 provides for that, given probable cause to believe that someone is violating the law. ---
Not everyone solicits prostitution on private property behind closed doors.
Who claimed they did?
The public/commercial aspects of prostitution are quite easily & constitutionally regulated by the State.
In the case you've quoted, the State/County were doing exactly that,
-- and I have no problems with Monroe Counties actions.
Then you have no problems with a state outlawing prostitution.
"Such laws [outlawing prostitution] cannot be enforced without violations of other individual rights."
"and I have no problems with Monroe Counties actions."
The Monroe county actions enforced the prohibition of prostitution, which you said couldn't be enforced without violations of individual rights, and yet you have no problems with those actions. You're a mess. You're all over the place, like a caged thrashing animal.
The Monroe county actions are not attempts to "regulate" prostitution. They are prohibiting it.
You forgot that a cop can get a search warrant to stay within compliance of the 4th Amendment, when enforcing laws that prohibit prostitution.
A third grader would have a better understanding of the law than you have.