I think "Between the Lions" was more structured like "The Electric Company" than "Sesame Street". Like "The Electric Company", it focused more on phonics and taught children to read, while "Sesame Street" was more teaching the basics, such as the alphabet, shape recognition, and counting to twenty, among many topics. Although I did learn on Muppet Wiki that "Sesame Street" did have some phonics segments in the 1990s, such as words starting with "SH", "CH", etc., and even a Waiter Grover segment involving "ch" words. But those phonics segments were not used as extensively as on "The Electric Company".
I agree that certain series can make a comeback, if not with live puppets. Shows that relied on puppets over the years can be revived with 3D computer animated characters instead of live puppets. "Mister Rogers' Neighborhood" used puppets in the Land of Make-Believe, and the spinoff, "Daniel Tiger's Neighborhood", used 3D computer animation. I am not sure how Daniel's show is doing in the ratings, or whether or not production had ceased.