> The university insists that homework can't be optional, but it lost its meaning. I've tried to explain to my students that it's in their interest to think about home assignments on their own, but the majority will obviously use gen AI, and it's such a waste of time to check and grade LLM output.

Can't you just not grade it at all? If the student has done their homework, just consider it passed. And then don't count it at all for the final grade.