For homework: if you make homework results not count towards the final grade, then there's no reason to use an LLM - the point then just becomes to have practice problems and feedback on how well you are doing.

This is what my university (EPFL) was doing ~40 years ago. And yes, some students didn't bother with the homework, and mostly paid the price at the final exam...

Yes. I've tinkered with the idea of non-graded homework, too.

Unfortunately, if I give homework that will not be graded, almost no one will do it. But I WANT them to do it for the practice it gives them.

The only reasonable answer I could find is to award them full points for simply doing the homework on time, even if it has errors.