I remember hearing an actor in an hour-long television series talk about this same sort of thing. It was a fantasy in which some characters inhabited one world, and some inhabited another, and a very few crossed back and forth. He was one of the main characters and one who crossed back and forth between the two worlds. One day, one of the producers (or directors--can't remember!) came over and said, in a nice-ish sort of way, "Hey, I noticed you've been a little slow to some of your scenes lately. We're trying to watch the production budget...blah, blah, blah." And the actor stared at him in amazement and said, a little angrily, "Well, yes, but that's because I'm IN every scene every week! And I'm just trying to make sure that I'm ready for my next scene because my head's still in the last scene we shot!" And the producer (or director--can't remember) was, well, stunned. "Really? You're in every shot?" And they looked at the scripts and he realized that the actor was pretty much on-screen the entire time. It was grueling schedule. So they started trying to find ways to build a little time into HIS schedule by shooting things that DIDN'T involve him in between all the things that DID. The point I'm making is that Kermit is on stage a lot! Whatever is happening usually centers in some way around him. The best example I can think of is in TGMC, when he was either on stage with Fozzie, or onstage with Piggy (I realize that Frank was doing double-duty also), but he was almost always on stage (Okay, okay--on camera. Sheesh. Picky, picky.) So I think the challenge would be to find scenes that involved Rizzo that didn't also involve Kermit (or some other Steve character). My first thought was to have had the rats happily squatting in Kermit's office in The Muppets, but of course Steve does Statler now, so that would have been somewhat challenging. (Steve and Dave are just wonderful cronies as Statler and Waldorf--a good pairing between those two fine muppeteers.)
I LOVE Rizzo, and most of us feel like Rizzo is one of the original The Muppet Show characters because the little guy has just gnawed his way into our hearts, and because he was a new character that came to us in one of the movies and stayed (unlike the frogs from marketing, who just went back to wherever they came from, mostly). And his easy friendship with Gonzo sort of cemeted that deal, officially branding him as one of OURS. (Another great Steve/Dave buddy pairing.) So Rizzo feels like home folk--and has earned that right--and I DO miss him a lot when he's not around, but I do understand. I am guessing, but I'll bet if you asked STEVE if he would like a sit-down for a few, or to do some scenes with Rizzo instead, that he'd probably opt for hanging with our favorite rodent--but it's probably not always up to him.
I'm enjoying Steve's Kermit more and more, but Rizzo can be a guest at my table any day he wants. Let's hope our favorite household pest gets more to do in the NEXT movie. (Yay for NEXT MOVIE!)