Well, it seems to me, every single problem with Muppets Tonight was conceptual. I rewatched some episode someone posted on Youtube, and I just can't help but feel that Kermit's character comes off as Producer that somehow interacts with the rest of the characters. they wanted someone hipper than Kermit to Host the show, and Clifford was what fit the bill.
Looking back, I think they should have drilled the point in that Kermit was too busy to be on his own show, except for certain segments. It seeems more like a "Muppets: The NEw Class" than an honest to goodness sequal to The Muppet Show. I remember reading a quote on the muppetwikia page that said that they finally got the show the way they wanted to, in a place where it worked, after they finally cancelled the show.
So, I really can't blame Clifford for taking over the show, so much as being the character that had to carry on the legacy of many characters who just weren't featured regularly. Oz's characters only appeared every so often, and Gonzo, Kermit, and Rizzo were the only regular classic characters to appear in every episode. Even Miss Piggy wasn't around too often. The burden laid with the new puppeteers like Bill Baretta and Leslie Carrara, so naturally, it would wind up focussing more on newer characters.
Personally, now I miss seeing the character. Kevin is too busy with Sesame Street. Not just Elmo, but all the titles and duties he holds. His last appearance was a dubbed (or so I've heard) cameo as a bouncer in MOZ.