I agree that something like this would be very useful. I tested out what ChatGPT could do regarding cheating in a very minimal way. It relates closely to your point 2. The thesis was to rate how likely an answer was to be generated by AI, similar to how programs will rate how likely an answer was plagiarized from the internet.

I took a refined response to AP test questions from a teacher and a generated response from ChatGPT, both very good. If I simply asked if it was a student or ChatGPT, with the note that some students would be very intelligent or very educated teachers acting like students, it would either say both were generated by a student or ChatGPT. However, if I asked it to rate the likelihood it came from ChatGPT on a scale from 1-100 I got good results with it ranking the teacher’s response lower than ChatGPT. The score for ChatGPT was in the 90s typically where the teacher’s were 70s or so.

I think refining this functionality would be one way to provide a solution which scales, at least theoretically, infinitely.