I'm considering each Muppet's role in the story, too.
Yes, Kermit's there, but he very much plays a supporting role. Whitmire isn't tasked to do an entire movie as Kermit right out of the gate.
Beaker appears, but very briefly. He and Bunsen don't do any of their major schtick. There's that lovely scene of Beaker gifting Scrooge his scarf (a final gift from Richard?)
Janice is present, but in little more than a cameo. Same with Animal. Piggy and Fozzie have much less to do in comparison to their normal roles. Sam has one simple scene. Each is basically only in one scene and setting, just enough for Oz to stop by, do his thing, and then go back to directing his own stuff.
Then, they made Treasure Island and we can see this strategy evolve. The primary leads are the human Kevin Bishop and Tim Curry, and the two are given multiple scenes without Muppet support.
Of the Muppet performers, Goelz and Whitmire are again pushed forward with Kermit having a larger--but still not huge--role.
Oz's characters are used a little more, but that's only because Kevin Clash is the one performing them on set. Clash also picks up his own major character of Polly Lobster. Bill Barretta likewise gets Clueless Morgan, and Nelson's main character is Mad Monty. Nelson also gets the opening scene for himself as Blind Pew. All brand-new characters.
The Chef, of course, has only an obligatory cameo ("How else did you think we were gonna get him in this movie?") and the Electric Mayhem basically only play background music. The two members who speak are Zoot (Goelz) and Floyd (Nelson).
This is the late-90s Muppets stable of performers. Whitmire and Goelz are pretty much the leads, Nelson does a few old staples and a few new one-offs, Oz's characters are used sparingly, and the new kids (Clash and Barretta) get a chance to show off their stuff. It's how Muppets Tonight and Muppets From Space were cast as well.