A key issue would be accounts. It would be a pain to have an account for every class. If it’s one instance with many communities, it might discourage people from participating if everyone in the school can see what you do. Tools like Piazza make it easier to deal with these issues, and they have a lot of other tools specific to courses.
If it’s a general instance for the entire school, then an instance run by students and unaffiliated with the school would be best. Otherwise students wouldn’t feel comfortable using it. I help with the community for my university (UBC) And there’s a lot of content that wouldn’t exist if it was an official thing (reporting issues with professors, asking for help with academic/mental health/relationships, sharing news critical of the school, etc.)
I really do want more academics on the fediverse, but “Lemmy for school” doesn’t feel that useful