The one thing that endangers a newer skit becoming a classic is when the references become dated. I love skits like Meal or No Meal and Pre-School Musical. But the shows they've been based off of have disappeared as mysteriously as they started.
I had no idea those were no longer popular. Maybe it helps that I never watched either show.
But I don't think being a dated parody makes it bad for modern viewers. As a kid I was a big fan of the Miami Mice segments, but had never heard of Miami Vice. I also enjoyed Monsterpiece Theater, though I can't remember if I knew about Masterpiece Theater when I was introduced to Monsterpiece. But either way, I wasn't aware of very many of the productions spoofed for Monsterpiece Theater until I was much older. I also didn't know they were parodies (if I knew what a "parody" was).
Kids can enjoy dated parodies of things they know nothing about. How many of us enjoyed The Flintstones and the Warner Bros. Honeymousers cartoons as kids without knowing about The Honeymooners? Or the WB short The Mouse That Jack Built without knowing about The Jack Benny Show? And all those caricatures of celebrities (both of the actual celebrities and parody caricatures) who haven't been famous since the 1960s or earlier....
In fact, as an adult, many of the parodies on Sesame Street these days are of things I am not familiar with. I can't remember if I knew about Mad Men when that was spoofed, but I'd never heard of True Blood, The Deadliest Catch, Boardwalk Empire, or Downton Abbey until they were spoofed on Sesame Street. I guess it helps that the shows are genres I don't watch and I think they all appear on premium channels I don't have. I only vaguely knew about Homeland before seeing the Homelamb parody online today. I know that "Good Things Come to Those Who Wait" is supposed to be a parody, but don't know what it's a parody of (I know I can just check Muppet Wiki to find out).