Is it just me, or does it seem like, around season 10, when they started to get more performers to be on the Sesame Street set on a full-time basis, a lot of the newly-introduced characters were primarily used in street scenes and rarely in inserts? A lot of characters during this era were only on the show for one or two seasons, I guess by putting them only in street scenes, there weren't really any inserts with the characters to continue running (though the street scenes could re-air a season later).
A lot of new characters of the early 1980s, particularly short-running characters, were used a lot more in street scenes and hardly in inserts. Characters like Aristotle, Mona Monster, Ferlignhetti Donnizetti, Dexter, Professor D. Rabbit, Barkley (maybe as often as characters like Big Bird or Oscar appeared in inserts), Bruno, Countess von Dahling, Gilbert and Sullivan, Countess von Backwards, Poco Loco, and others.
When it comes to short-lived characters who mainly appeared in inserts, all I can think of off-hand are Leslie Mostly and Pearl. A few seem more half-and-half. Telly and the Honkers were in a lot of inserts as well as street scenes as early as season 12. Deena seems like a sketches character but appeared a lot more often as a solo character in street scenes than as part of a duo with Pearl in inserts (only four segments, and only one is known to have been repeated so far). Elmo is an interesting case. As the wiki's proto-Elmo page says, whenever he appeared in inserts during the Brian Meehl/Richard Hunt eras, he was treated more like a generic Anything Muppet monster and performed by whoever, but when he was in street scenes, he was named Elmo, had a regular performer, and had something of a personality. And then when Kevin Clash took over, he almost immediately started appearing in inserts in that form (okay, it took a season before Clash was performing Elmo in inserts, but he got at least three in season 17).
Another interesting case is Dr. Nobel Price. During his first season, he was in a few Newsflash segments while also appearing in street scenes, but after season 12, he only did one more news segment, while he continued being a "street scenes character" for another 8 years. Forgetful Jones and his crew are another interesting case, as season 12 had them in an almost equal amount of inserts and street scenes (well, Buster wasn't in any season 12 street scenes), and it would continue to be this way through season 23, but I don't think any of the season 12 Forgetful Jones segments re-aired on the show after Richard Hunt took over the role. And they waited until season 16 to remake some of the sketches so Hunt would be Forgetful - but it looks like only two of the Michael Earl segments were remade.
On another topic, it's clear that when some of the early Monsterpiece Theater segments had their Alastair Cookie portions redone, they were all done in the same session, as the chair is green in those, but otherwise the green chair wasn't used in MT (not in original versions of segments). I would think that in the 1990s, they'd have Frank Oz do several MT segments in a day (whether they just did the intros on those days or did the entire segments). It's a little weird that they did not re-shoot them on a day when they were doing new Monsterpiece Theater segments (unless they specifically wanted something to allow people to identify if it's an altered segment).