Tell the students that they will receive a one week notice during the middle of the semester that they need to migrate their git repo to a new server, then teach them the 2 or 3 commands they will need to enter to do this.

They will then understand that it is extremely easy to move a git repo.

It's just an educational exercise to teach students to setup and mantain their own git server.

Obviously students don't expect to use uni servers forever. They can setup their own with the lessons learned.

Probably but I never got why that is. It seems a school could be there in all kinds of ways for the entire duration of the career.

Any Git clone is also technically a Git server, so no, they don't lose access to their own filesystem after graduating.