Well, money solves a lot of problems, doesn't it? And if the muppets are flush with cash all the time, then some of the problems they encounter could be easily solved, ruining the story. In TMM, they could easily have just chartered a bus or a plane or whatever to take them where they needed to be, and avoided all the cross-country mayhem which makes up the bulk of the story. In TGMC, the fact that they are jobless and penniless makes it essential for them to locate and inhabit the Happiness Hotel, which causes them to rendevous with all the other characters, and also creates humorous alarm in Kermit when he sees the prices of the food at the supper club. In TMTM, their lack of money and food causes them to disperse and seek out other jobs elsewhere. It also causes Kermit to take a job, where he meets Jennie and their story goes on from there.
In later movies and shows, poverty of one sort or another is one of the driving forces of the various stories. If Jim Hawkins had money of his own, he wouldn't have to seek for buried treasure! If Bob Cratchit had money of his own, he wouldn't have to worry about Tiny Tim not getting the medical help he needs, or worry about missing a day's work--and pay. In IAVMMC, money would solve the entire problem, wouldn't it? (I always imagined that Piggy could have simply cashed in one of her investment bonds and bailed them out--she had SOOO many endorsement and products in the 80s...) So the lack of money and the problems that lack creates adds dramatic tension to the story.
Anyway, probably a far more complicated answer than you were interested in! Auntie Ru tends to babble a bit.