It seems like Kermit segments were becoming scarce before The Jim Henson Company sold the characters to Sesame Workshop. I watched season 30 almost every day and felt like the appearances of old Kermit segments were few and far between (they showed Kermit and Joey singing the alphabet, ABCs of the Swamp, Carribian Amphibian, and a few News Flashes, including Rupunzel, Christopher Columbus, Peter Piper, and Sleeping Beauty putting the prince to sleep).
Back in the 2000s, when the only Kermit material shown was Do De Rubber Duck and Everybody Be Yo'Self, where Kermit is really just part of the gang, I wonder if kids felt confused, seeing Kermit there when he wasn't shown much, when he's much more familiar as part of the Muppets. Were the kids of the 2000s confused when they saw new Sesame Street DVDs that featured Kermit segments, particularly ones that had multiple Kermit segments? Ditto for if they saw older videos that had Kermit in them. Or would they just be excited to see Kermit on Sesame Street (when I was a kid, I was excited to suddenly see Pee-Wee Herman reciting the alphabet and making a couple cameos in the "Put Down the Duckie" number, and was happy to see The Simpsons show up for a cameo in "Monster in the Mirror").