Jonah, you probably already know this, but not having a good name to lose isn’t just a PR matter — it comes up in libel and defamation cases. (The one area of law I know a little about is libel; when you’re a newspaper editor, you get threatened with a lot of libel suits — a lot more than you do as a fairly controversial political commentator, weirdly enough.)
Some plaintiffs have been held to be “libel proof,” i.e. having such low reputations that they cannot suffer meaningful incremental harm to their reputations even in the face of claims that are false and ordinarily defamatory.
The New York Times has argued that Trump is “libel proof” on the matter of touching women in an unwanted sexual manner. Mobster John Cerasani argued that he was defamed by the film Donnie Brasco, but the courts decided he had no good name to damage. Bob Guccione lost a libel case against Larry Flynt, whose magazine had suggested that Guccione was — you’ll find this difficult to believe — engaged in extramarital sexual impropriety.
A similar case was made — unsuccessfully — by a scurrilous journalist rightly sued by William F. Buckley Jr. in response to his claim that WFB was a “fellow traveler” with fascism.
My own view is that public figures should probably be more aggressive about libel cases. They won’t help their reputations much, probably, but it is a public service to call to account journalists and others making claims that are false and defamatory.