My guess is that reason is that Moonlight Sonata is not hard to learn, just tedious to teach a beginner, because of the endless repetition of relatively short phrases shifting and changing a little bit at a time.
This is what makes it fantastic, but learning to play it is mostly learning a few phrases and recognizing the shifts, which I can imagine would drive your teacher nuts until you're at a stage where you can pick up the changes rapidly enough sight reading to not have to remember every transition.
I'd guess - as a very mediocre piano player - that it's as a result low "bang for the buck" for a beginner on top of annoying to your teacher.
Upside is once you get even just relatively mediocre at sight reading it's fairly simple to work your way through yourself.
Whilst the first movement is fairly technically straightforward, the last movement is pretty tricky and requires solid technique; I certainly wouldn’t characterise it as “easy” even if it’s not the hardest piece in the repertoire.
If anything, the issue is that as a whole, the piece is fairly technically demanding, but the first movement is simply enough for most intermediate pianists to sight-read, so something that seems approachable soon becomes impossible for anyone below a certain level.
I can buy that it's technically demanding to do the last movement well, in the correct tempo, but learning it to a standard a relative beginner will be happy to achieve was not hard for me. But that may well be another distinction that makes it frustrating for a teacher to try to teach to a beginner, because, yes, it will likely be noticeably flawed.
This is what makes it fantastic, but learning to play it is mostly learning a few phrases and recognizing the shifts, which I can imagine would drive your teacher nuts until you're at a stage where you can pick up the changes rapidly enough sight reading to not have to remember every transition.
I'd guess - as a very mediocre piano player - that it's as a result low "bang for the buck" for a beginner on top of annoying to your teacher.
Upside is once you get even just relatively mediocre at sight reading it's fairly simple to work your way through yourself.