And it wouldn't be a proper Muppet movie if the gang wasn't on the move. So getting mileage out of the heist genre ("Is this going to be one of those comedy heist bits? I hope not—those never work!") makes good plot sense for a Muppet sequel.
Muppets Most Wanted is also a sequel in another sense: it has the same sense of humor. Jones' biography notes that Jim Henson insisted that the Muppets' comedy was, at its core, visual. This had to do with how the puppeteers played a punch line, but also the ways the design of the Muppets could be manipulated as well.
This may help explain why Tina Fey is so great in this movie. As a Saturday Night Live veteran, she's well versed in sketch and variety comedy. She is an excellent comedic performer, in a physical sense. The sketch—the short comedy scene—depends on the actor's ability to embody a joke the whole way through to the punch line.
Muppets and SNL cast members are doing much the same thing, in a lot of ways (and Henson was in fact a frequent visitor to SNL). So it's natural to pair Kermit and Nadya together to create a talent show, and it's funny, to boot.
The doppelgänger villain seals the deal, locking in this installment's absurdist, burlesque, and self-referential humor. The Muppets can't recognize Constantine isn't Kermit; Constantine's attempts to imitate Kermit play on a self-referential exaggeration of Kermit; or Constantine's fugitive heisting gives the movie ample opportunity to caricature the heist genre itself. Constantine looks exactly like Kermit in one sense, but his behavior—including his posture and gestures and mannerisms—is wholly unlike Kermit.
This all hits its peak when Constantine practices his best rendition of Rainbow Connection, but can only muster this imitation: "the lovers, the dreamers, and cheese" ("nailed it!"). The qualities that define Muppet comedy are all bound up in the moment. Constantine is the alter-Kermit.
If The Muppets might be considered a variation on Henson's intention to intermix man and Muppet in new ways for the movies (best summarized in "Man or Muppet?" and the eventual resolution for Walter), then I think this sequel focuses on being a sort of answer to that first question: what holds the Muppet family together?
And Kermit is its way of answering that question.
Jones notes that from the early days Kermit "was the sun around which the entire Muppet solar system revolved," and (quoting head writer Jerry Juhl) goes on to say, "More important, [the other Muppets] have to relate to him. Without Kermit, they don't work. Nothing could happen without him. The other characters do not have what it takes to hold things together . . . . Kermit's the organizer, always desperately trying to keep things going while surrounded by all these crazy nuts."