Local models are possible and nothing in that area of development will ever publish a hash of their output. The huge frontier models are not reasonably self-hosted but for normal K-12 tasking a model that runs on a decent gaming computer is sufficient to make a teacher's job harder. Hell, a small model running on a newer phone from the last couple of years could provide pretty decent essay help.
Heck, use a hosted model for the first pass, send the output to a local model with the prompt "tweak this to make it sound like it was written by a college student instead of an AI"