I've noticed that on the new show, there seems to be a small group of characters used (even if it's a big small group). In nearly every episode (until the last two, which have had certain major characters absent), the characters seen in practically every episode are Kermit, Miss Piggy, Fozzie, Gonzo, Rizzo, Pepe, Scooter,Dr. Teeth, Floyd, Animal, Janice, Zoot, Lips, Statler, Waldorf, Bunsen, Beaker, Sweetums, Sam, The Swedish Chef, Yolanda, Chip, Big Mean Carl, Bobo, Andy, and Randy, with Lew Zealand, Crazy Harry, Beauregard, and a few minor monsters sometimes showing up (rarely at meetings, though). We have seen other characters make appearances, but Denise hasn't shown up as frequently as we expected (though it seems she's there more in the past few and upcoming episodes), and Rowlf's appearances have been scarce (especially considering he's the owner of a tavern, which I think Bill Prady made a big deal about in interviews).
But then something hit me about the shortage of other characters. On this show, nobody has a "standard" outfit. Every day, each character wears a different outfit, though naked characters are still naked most of the time (I don't think we've seen Kermit in any clothing on this show yet). Some characters do wear the same thing most of the time - Uncle Deadly usually wears his original clothes, The Swedish Chef usually dresses like a chef, Bunsen and Beaker usually wear their lab coats (though there was one time in Hostile Makeover where Beaker was wearing a dressy shirt around the office for no real reason).
I'm guessing that could be why a lot of characters haven't shown up, because then they'd have to make a lot of different outfits for many minor characters.