IMO this kind of thing adds work and stress for the best students. If I'd been faced with something like this while I was in school I would have felt the need to basically curate a parallel construction AI discussion, knowing it would be judged. I understand the theory that, in the age of AI, the prompts are more interesting than the outputs, but I'm not convinced this is the way.
Things like the Denmark approach (and/or in-person written responses) seem like a better direction. Treat take-home writing the same as we've treated take-home math questions - as useful practice (for those who choose to actually engage with it), but not a significant input to grading.