I also agree that MT was hit and miss (especially season 1). I remember somebody (possibly Steve Whitmire?) mentioning that the reason why MT was so heavy on new characters was to breed new life into the Muppets. I'm guessing it was felt that adding a lot of new characters would have made 'new life' for the Muppets easier. Characters that worked could be added, greatly increasing the Muppet family, while characters that didn't work could be dropped.
I agree that the lack of classic Muppets was quite a loss. I remember a few episodes that Kermit wasn't even in (outside of the intro). But it was always fun whenever Kermit and other classic characters got to do things away from the studio (such as Kermit's date with Gilbert Godfrey). I really want to see the Muppets in more of sitcom situation; MT and a handful of TV specials may be the closest we get for now.
Gonzo also seemed to be used less on the show. Again, there were a few episodes that he wasn't in, but I really did enjoy Gonzo's new crazy stunts. To me, even with the presence of several new characters, Gonzo still stole the show whenever he was on.
I really wish that Bunsen and Beaker had more to do on the show. The Andie MacDowell episode is one of their few episodes, and definitely one of their best. It really gives us a chance to see other sides of both Bunsen and Beaker, and again, returns to that great 'sitcom' feel of the show.
Rizzo had quite a bit to do on the show. This was most likely done so that Steve could flesh out the character more. Rizzo was basically to Clifford what Scooter had been to Kermit.
The lack of other classic characters mostly had to do with characters not being recast at this early stage (although Bill Barretta does one of his first performances as Rowlf in an early episode). And, of course, there was the fact that Frank Oz wasn't always available.
The remaining 'classic' characters either were in the background, had one (or two) time cameos, or were not seen at all. Bean Bunny had a couple of cute (no pun intended) bits, as did Beau and Lew.
Most of the new characters were really great. The writers, producers, and performers made wise choices in deciding which MT characters could actually remain in the Muppet family. Pepe, Bobo, Johnny, Sal, Dr. Phil, and even Carl and Howard were great additions to the group. Though I do wish that a few other characters had stayed on (Seymour, Nigel, Eugene, Mulch, Darci, Spamella, Carter, and maybe even Bill the Bubble Guy-despite being a one joke character, but hey, so is Lew Zealand-and some of the guys from Deep Dish Nine). Mr. Poodlepants (who is clearly meant to be a parody of comedian Ed Wynn), while a funny looking character with a great voice, did seem a bit bland. Andy and Randy were great one-joke characters, but eventually overstayed their welcome (the writers must have noticed this, as they seemed to be used less in season two). Zippety Zap (again, a great looking character with a fun voice) seemed like a character whose material could have easily been given to Floyd. As much as I love Kevin Clash, I thought Mulch's constant growling was a bit annoying. Though I don't mind having Mulch there. In fact, I actually like the character, just not his growling.