You forget things can be signed, with the key owned by the school. It can be done.

Does signing really make this easily auditable from the professor’s perspective?

Exactly this, when was the last time a HN user had to interact with the prototypical 60-year-old set-in-their-ways professor?

Extremely non-tech savvy, hates computers, and is gonna grumble "What the hell is a PGP? Better not be another one of those phone code things." as you try to pitch this highly-technological solution to a largely niche problem domain.

I mean a cloud based learning management system also seems to be a very technological solution to the very old problem of checks notes grading quizzes?

They don’t even need to not be tech savvy. This stuff just registers as “hassle” to most people so they do the bare minimum or search for ways to not deal with it at all. It’s easy to “tut tut” at them but ultimately we need to accept reality: privacy, security, these things take extra effort that isn’t strictly necessary for people to go about their daily lives even though the stakes can be super high. It’s not a problem until it is, so they aren’t really barriers that require people to do the work. It’s like convincing someone who just simply doesn’t want to go out and buy/install a lock on their door to go do it, except it’s not even a one-time thing. Their door works fine. They can come and go as they please. It’s not until something happens that they maybe change their tune (and even then!)

Hell just getting people to do secure passwords is a whole thing.