If the law is not enforced it's no different than there being no law, choosing not to enforce the law or delay enforcement because the perpetrator is wealthy or politically connected happens in oligarchy not democracy.
According to Wikipedia, only 2 people have ever been charged under the act in over 200 years and neither was convicted, so it's not really a law at that point
Nobody has ever been found guilty of violating the Logan Act. Nobody has even been charged with it in over 150 years.
Why? Probably because prosecutors realize that in the modern era, a 1798 law that bans "commencing or carrying on any correspondence with a foreign government" would almost certainly be struck down on First Amendment grounds.
It bans "correspondence or intercourse with any foreign government or any officer or agent thereof, with intent to influence the measures or conduct of any foreign government or of any officer or agent thereof, in relation to any disputes or controversies with the United States".
Trying to influence others is fundamentally protected by the First Amendment, even if (especially if!) your interests are not the same as those of the government.