The biggest thing that would hamper a prosecution would be their inability to subpoena the records of the website, thus depriving them of the key evidence they need to tie the individual to the site.

Also, a strong First Amendment defense could be mounted to stop the prosecution.

(still not a lawyer)

would have anything to do with the legality of operating the business from the United States? If the US citizen is violating federal law by operating this website, and fed LE decides it wants to prosecute, they certainly could, for example, indict him for violating the Travel Act. Where do you think those ads and reviews appear?

      Talk to the CEO of Poker Stars who got arrested the minute he flew into Dallas. His foreign servers and bank accounts and even foreign operation of the business did not help much given that he facilitated gambling in the United States.  Can you see the analogy?

      The only thing operating foreign servers give you is the host country may not be obligated to honor a subpoena or arrest warrant received from US authorities, depending on the terms of the Mutual Legal Assistance Treaty between the  countries.  But it is easy to trump that protection by indicting the guy for some crime other than basic prostitution, such as money laundering