Schools need to re-think what the purpose of essays was in the first place and re-invent homework to suit the existance of LLMs.

If it's to understand the material, then skip the essay writing part and have them do a traditional test. If it's to be able to write, they probably don't need that skill anymore so skip the essay writing. If it's to get used to researching on their own, find a way to have them do that which doesn't work with LLMs. Maybe very high accuracy is required (a weak point for LLMs), or the output is not an LLM-friendly form, or it's actually difficult to do so the students have to be better than LLMs.