Or even just set up a "computer cam" that films yourself working.

This is what it's come to with digital art hasn't it? Artists recording their screens.

Due to the nature of the art process it's not uncommon for artists to stream live on youtube/twitch with some music and get a decent number of viewers. Sadly the same wouldn't apply for writing I think.

Yeah, but what if they have a bag of chips, and inside that bag of chips, is a small tablet or phone, in which they ask chat gpt to give them the essay, and then they transcribe it? They might even eat some of those chips to obfuscate that they're getting the information from the bag.

At some level, there has to be some trust, or a system (e.g., in person proctored exams) would have to be used instead.

I bet students would start to print out the plagiarized essays and retype them. If the plagiarists made an effort to make minor changes and rearrange things as they went, no screen recorder or edit history could distinguish it from normal essay writing.

I believe you just described the typical student paper writing process relatively accurately.

I would try to pass the teacher's message through an AI checker, then answer "Sorry, I can't accept your comment because it was 34% written by an AI, and I only obey to my teacher, not ChatGPT". I don't know if that would work, but that's very clearly the kind of thing I would have done when I was a teenager.