I wouldn't like it, because in DD's case, it's a cure looking for a disease.
I recognize that my kid is not the target of these assignments.
For the reading logs I've encountered, the kid has free reign on what they read. Reading 20 minutes builds endurance and reading vocabulary. For a kid like mine, it's an excellent exercise to get my initials daily and to keep track of her daily responsibilities for school.
Bostonian, there a lot of kids who won't do it or will make it up, there are kids who will read anyways, and there are kids that are reading -- an additional hour and 40 minutes a week -- that they wouldn't otherwise read. That time adds up over the years.
I was one of those kids who didn't read voluntarily until 7th grade. Such logs served me quite well.
