Each time it comes up, I start with ignoring the log altogether. If the teacher is paying attention he or she quickly realizes that my son is a strong reader and doesn't need the log. If the teacher insists, then we just make something up, write it down and move on.
I'm not sure what lesson my son is learning from this, but I'm sure it's not what the school is hoping for.
This really fucked me in college. I never learned how to study, just how to memorize things from a quick read and complete the minimum to pass a class. When I went into an engineering college, this fell apart around the fourth semester, as I was getting slower and slower during tests. Since I didn't study and homework wasn't mandatory to pass (or so I thought), I never really learned material until I saw it on a test. I learned a lot on tests (and I like working under pressure), but as the difficulty of the material increased, I wasn't able to teach myself at test time. This devolved quickly, and I left college.
tldr; homework's portion of your grade doesn't matter. Learning the habit to set aside time to work outside of what may appear to be required is the real skill. If you choose to encourage skipping homework, please impart this habit in some other way. It is not obvious to each individual, no matter how quickly they might grasp certain subjects.
I did some homework during the school day, generally at the expense of listening to the teacher lecture. Or, I jammed in some last-minute homework over lunch (half-assed effort simply to get credit for having attempted something).
It didn't impact my grades much. I was an A/B student, probably could have been straight-A if I wanted to be, but preferred playing sports, or just being a kid/teenager.
I had enough honors/AP course-work and extra-curricular activities to make up for slightly less-than-stellar grades. I ended up at the top public university in my state, alongside many of the straight-A students. Could I have gone to Harvard or Stanford with better grades? Maybe. But I probably would have gone to UVA regardless because of cost.
I learned everything I was meant to except for one: I never learned to be disciplined about work and how to study efficiently.
When I started university, my CS classes were fine because that was stuff I did for fun and had done since childhood, but my electives, like maths etc. suddenly took 10x the amount of effort I was used to putting in.
In retrospect I wish I'd been pushed to do more work. Not necessarily harder, but more.
I'm not saying I wish I'd spent all my time on homework, but getting used to actually having to work for things earlier would have made the transition a lot easier.
I was a few questions away from a perfect score on my SAT and had an app with over 2 million users so I still got into a good college. So it is doable and I would still encourage others to refuse to do homework.
For late elementary and junior high, I don't remember whether or not homework was a large enough part of the grade to fail you if you took a 0 on all of it. In high school, I think homework was a small portion... something like 10-20% of the grade. So you could blow off homework if you aced everything else. You had to get at least a 70 average to pass (we didn't do D grades), so if homework was 20% then you had to get at least an 88 average on everything else in order to pass the class. And I think I have vague memories of homework being 30% in some of my high school classes, which means you'd have to perfectly ace everything if you wanted to take a 0 on all your homework.
And there could be consequences for extracurriculars if you were taking low grades in your classes. I remember that in junior high, you could only go to the school dances if you had at least in 80 in all your classes, and in high school, if you were failing even one class you couldn't participate in any school sports.
Worth pondering this phrasing, I think.
EDIT: and I forgot to mention, I'm just one half of his parents. The other half doesn't believe what I believe. I am in the vast minority in my city.