I've always been a huge fan of "Alternate Universe" or "Dark Universe" versions of usually light characters (Star Trek does it, the Muppets do it there...) It really highlights the brightness of their normal selves and develops something about the character. (Although Gonzo's darkness seemed to follow him back and get stuck to him for Mwoo and LTS too!)
Think of it this way... if you felt that the alternative timeline was disturbing, think of how disturbing it was for Kermit (though I'm sure he enjoyed seeing Mr. Wholesome All American Sam as a rave monkey). I don't think it would have had the same impact if the rest of the characters were just kinda bummed or something. Like if Biff Tannen becoming rich made Hill Valley a futuristic Utopia and Marty's mother being happier with Biff than she ever was with Mr. McFly.
Would you believe there was some television show (or cartoon or movie, I forget which) that did a parody of "It's a Wonderful Life" and the town was all the better for someone not being born, and everyone thought it was pretty depressing and almost sadistic?
Though I will say some of the alternate versions of the characters make more sense than others. Fozzie being a pickpocket... works. After all, in the first movie he was seen at a very shady looking bar... hanging around the bad crowd, can't get any good work, falls on terrible times... Gonzo and Amy the brick. A depressed, suppress Gonzo who has no one appreciating his madness? Also works. But above all, Piggy's lot in life as a struggling actress who winds up taking a terrible, soulless job as a telephone psychic (could have been real blue there... even Rocko of Rocko's Modern Life wound up doing that), also being miserable and alone. Works best of all. Kermit and Piggy, as this movie proved, need each other. Kermit and Piggy give each other confidence and love. Without that, we get a depressed Piggy who's a shell of what she could be (VMX) and a very depressed Kermit who just doesn't care (TM)...if nothing else, THAT made VMX. Just ignore half of that sequence... it works better.