I agree that this situation that the author outlines is unsatisfactory but it's mostly the fault of the education system (and by extension the post author). With a class writing exercise like the author describes, of course the students are going to use an LLM, they would be stupid not to if their classmates are using it.
The onus should be on the educators to reframe how they teach and how they test. It's strange how the author can't see this.
Universities and schools must change how they do things with respect to AI, otherwise they are failing the students. I am aware that AI has many potential and actual problems for society but AI, if embraced correctly, also has the potential to transform the educational experience in positive ways.