The fact that the only consistent exposure to the characters for many years was in Muppet Babies form helped stuff their more clever puppet origins away in a cubbyhole. The Babies' property can't be blamed for the failure of the main Muppet thing going for so long, but it definitely was a factor.
I don't ever think I had that problem myself. The Muppets were always around some form or another. TV stations replayed the Muppet Movies from time to time, some stations reran the Muppet Show, there was the occasional special, that Muppet Magazine, and then there were videos. It could be that those people just watched Saturday morning cartoons and nothing else. I mean, when I was growing up, there were Muppets all over the place.
Now, the 90's saw a growing deficit. A not successful TV show, 3 not really successful movies, and that Disney/Henson VHS partnership that put out more Muppet babies and (oddly enough) Fraggle Rock videos than The Muppet Show. What, did we get 2 best ofs without celebrity guests and one Halloween special made out of the Vincent Price episode and the Alice Cooper special.