What is the point of grading homework for college students anyway? The objective of exams is to determine mastery of the subject. It makes sense to have a grade act as a certificate of mastery.

Grading homework is a measure of conscientiousness and perhaps a pedagogical tool to force learning but by college perhaps we should have moved out of the need for the latter.

One can simply measure conscientiousness through attendance grade and mastery through exam grade and then we have two grades the universities can certify students for that are no longer dimension reduced into a single number.

To provide feedback on mistakes and help them learn. Unfortunately if you use the grade to contribute to their overall marks, some will cheat.

But that's easily solved - just don't reward cheating on homework.

We did not have homework per se in what we studied but we did have reading that was relevant for the purposes of tutorials and being prepared for lectures. We also had deliverables (assignments, presentations, practicals) that had grading, and proctored exams.

I found having deliverables helpful in knowing how one is tracking with progress and understanding of the subjects and largely reflective of the final exam result.

I've also had studies done that exams were either 80 or 100% of the grading and that was a lot more stressful without any significant added benefit. In fact given that there were fewer or no deliverables, perhaps even worse mastery / retention after exam completion.

Homework grades are supposed to provide feedback and some incentive to do the work.

However, counting homework grades toward course credit also creates an incentive to cheat. It probably makes sense to remove (or at least drastically reduce) that incentive.