Okay, back when ‘fan fic’ was being invented and I was an irresponsible young college student, I committed a few Trekkie stories. But Star Trek was (is) a television franchise, an ever-evolving collaboration between the creator, the scriptwriters, the actors, and the suits in marketing. By its nature, there are no end of loose threads / missed chances / untold backstories waiting to be exploited. Kurt Vonnegut, on the other hand, is a writer with a style all his own; trying to re-create that style isn’t ‘fan fiction’, it’s pastiche.
Vonnegut invented Kilgore Trout as a prolific hack with a mind so empty and a soul so vacant that aliens could use him as a loudspeaker. I don’t think he’d have been pleased by the concept of “fans” attempting to channel their inner Kilgores, but I’m sure he’d have taken a certain sardonic satisfaction in the attempt.