> Borcherds said he currently grades on completion if a student hands in their homework.

In high school (2006) my physics teacher gave credit for handing in the homework (he checked it and handed it back, but no grade was assigned). Didn't hand in homework, you got a zero.

He knew then that if you assign grades to hw, people will cheat.

If I'm paying for Berkeley, the professor have office hours for me to ask questions.

Cambridge engineering had something similar called "standard credit" for minor assignments. You'd get the full mark by default, only losing marks if missing or egregiously bad. The exam at the end of each year carried almost all of the grade. It meant you had to engage with the work, but didn't turn it into an exhausting competition for the best coursework grades.

Yes I also had this in Uni at some point. Just going through the homework can be a huge effort. If the course is small enough, you probably don't want to hand in obvious junk/slop, especially if you're asked to present "your" solution.