Recently it hit me that a lot of episodes where the street scenes were repeated two years later are episodes that contain an original song in the street story. Episodes like 1663 which was repeated as 1899 has Bob singing about the Indiana farm he was born on, and the episode where Biff gets a bowling ball stuck on his thumb, with a song about holding hands, was repeated two seasons later. I believe the episode where Big Bird hosted a number four show, with "I Just Adore Four", was also repeated later, though I'm starting to wonder if the original performance of "I Just Adore Four" was later repeated as an insert or not (I know it's been in video compilations, but I don't think I've ever heard of the original being in an episode other than one with the street story).
I guess since they were writing original songs, they might have wanted to get some use out of the song and have viewers hear them again. I don't think it's so much the case when songs that have been redone many times were in a new street story. The first season had street scenes with characters singing established songs which were only in one episode, not to mention many early performances of One of These Things that seem like they were only in one episode each, but that song was reprised so many times they might not have felt the need to repeat those street stories (not to mention they didn't start repeating street scenes two years later until much later). The second season had a couple early performances of "Sing" that I don't think were repeated (the second known performance even has them acknowledging that it was sung a few weeks earlier).
Of course there's also some that weren't repeated. I'm not sure if episode 900 (based on Ernie and Bert's Sing Along) or the episode where the street scenes appeared in the Sing-Along video, but those songs were all either public domain tunes or songs that have been on the show before (I've also noticed, looking at the guides, that the first street scenes last a long time before getting to inserts). The episode where Luis and Maria get married also has a lot of original songs that I don't think were reused later (nor was the plot re-used). I wonder if the episode where Gina meets Little Jerry was repeated two seasons later (I kinda want to say it wasn't, because Gina and David were only on the show together for two seasons and I doubt they would have repeated any David scenes after that). The episode where Gina writes in her diary wasn't repeated, but "Put It in the Trash Can" was repeated as an insert. I think there were other episodes with songs as part of the street story where the songs became inserts. And I'm not really sure about the episode with "Happy Tapping".
While not a musical number, it seems like Elmo playing musical statue was part of an episode with two separate stories. It was originally part of episode 3156, which for the first half has a plot involving the Furry Arms Hotel and the second half has a plot where Gordon tutors Carlos, the Elmo segment is pretty much stand-alone, but I recently found that that street story was repeated in season 27, with the statue segment included.... and looking at what Muppet Wiki pages the image links to, I didn't see any other episodes linked (and now the wiki has full rundowns of pretty much every episode past season 22, I even found that there's no longer any pages missing segments cut from HBO or Sprout, and none of the episodes airing as part of Noggin's 123 Sesame Street are missing segments, either). Though it has been uploaded online by Sesame Workshop and was included in a Play with me Sesame DVD (I think I also saw it in a Play with Me Sesame episode on Netflix).
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