I never thought of skits where characters just count to 20 (or 10, or 40) to be the number equivalent of reciting the alphabet.
Although whole numbers don't have a definite "end point" the way an alphabet does, counting up to some arbitrary high number from memory is similar in some respects: trying to remember a whole list in order, matching names to conventional symbols. Sesame Street still keeps a gap between "sponsor numbers" and "the highest number we can expect preschoolers to count", with those highest-number sketches always teaching the
whole list: 17 becomes just another step towards 20 (or 40, or 100).
Of course people don't recite the alphabet and stop at any certain letters (it would have been cool if Sesame Street had a recurring letter series with an opening where kids say the alphabet and stop at the featured letter, though Wanda the Witch begins with every letter up to W being shown).
People might recite letters that way if they're looking something up in a directory or dictionary, but that's the only real-life situation where I could imagine such behavior.

As for Sesame Street, I can recall three other classic clips that included characters stopping the alphabet at the sponsor letter:
- "The letter I looks like a bone": the boy in that cartoon stops the alphabet song at "I", although that might not count because the dog interrupts him.
- The "'J' Friends" song: one of the singers begins by reciting letters up to I, then asking everyone else what comes next.
- The "'K' Cheerleaders" clip: all of the cheerleaders recite the alphabet up to K, then cheer for their favorite.
There have been a number of recurring number skits that are basically the same except that they end when the skits get to certain numbers. One example is the animated series of sketches that has numbers that somehow resemble animals. I think some episode pages at Muppet Wiki refer to them as "number creatures", but I don't know the official title (for reference, the 20 segment was included in The Great Numbers Game). For something like this, where the numbers are being counted, I doubt that there would be any segments for one, two, or three... But I wonder what the lowest numbers are to have segments in these series.
I've seen Number Creatures segments as low as 11; that also applies to other sketches (Rubber Stamp, Carnival Masks, even the Count's "Number of the Day" song) that may end up at 20. Basically, for any sponsor less than 11, those sketches would never appear.