This is indeed the case for most anime, but some shows such as Pani Poni Dash! take place exclusively in the school, I believe Sayonara Zetsubou Sensei was also mainly done in the classroom during class, along with who knows how many other shows center around school teachers.
Then there's countless anime about student councils or school clubs
also, let us not forget that students struggling with homework is a common occurrence.
Yes, you are correct, although the majority of anime is centered around students, they don't as you stated, show the actual classroom environment much and rather skip over it, because the Japanese school system is legendary for being a overly strict hell like no other, but, at the end of the day, after all is said and done, these are still students we're seeing here, they in their commonly seen school uniforms are constant reminders that they do in fact attend a school, along with that quick rushing of the school period of the day, they might be rushing past it, but they're still showing it to remind the audience they are students who attend a school.
So I must ask again, why are NEETs, who are constantly being reminded of school, not offended by this?