> such a waste of time to check and grade LLM output

Small nitpick: you teach math, why don't you use an automated grader?

I agree homework should be optional and your college is wrong. Even without AI, for some students it's easy to cheat and maybe for some students it's a waste of time. Maybe you can assign it a very low score, like 5% of the final grade, and/or award the grade based on attempting rather than getting the right answer.

> why don't you use an automated grader?

LLM verifies output of another LLM. The circle is complete, and nobody has any doubts that this is just a theatre.

With manual grading, that one student who genuinely tries still has a chance to meaningfully engage.