I haven't read the book, so I don't know what the claims are, but it sounds silly on the face of it. I'll grant that some homework is busy work. But some homework is necessary.
You don't learn math by listening to a teacher explain it. You learn math by working through problems. That requires homework. You don't learn how to write by listening to a teacher talk about good writing. You learn how to write by writing essays out of class. You don't improve reading skills by listening to a teacher talk about a book. You learn by reading.
Maybe the claim is only concerned with younger children?
You don't learn math by listening to a teacher explain it. You learn math by working through problems. That requires homework.
You were fine until the last sentence. Teachers can and do assign practice to be done within the classroom. And practice time in the classroom has many advantages over homework. The primary one being that students are much more likely to practice problems correctly, and get help if they are going in the wrong direction. If the same student is assigned homework, the odds of correct practice strongly depend on the quality of adult assistance at home.
The important questions then become whether there is enough time spent in the classform for effective practice, and what the incremental benefit is or isn't from homework.
What does the research say? It says that once you control for parent's education and socioeconomic status, there is little correlation between time spent doing homework and academic performance. (Whether measured by future grades or standardized tests.) However within the population assigned large amounts of homework, the correlation between academic success and parent's education and socioeconomic status increases.
This is evidence that 35 hours per week spent in a classroom is enough time for teaching and practice. It is also evidence that homework on the whole doesn't help or hurt much, but does move responsibility for educational performance from the teacher to the parent. As a well-educated parent this is modestly beneficial, because moving more responsibility for my children's education to me gives my kids an edge. But at what cost?
The same research, unsurprisingly, finds very strong correlations between homework assigned and how much kids dislike school. High homework levels also result in significant increases in family conflict. The causes of both trends are so blindingly obvious as to not need discussion.
There is less research on homework versus academic performance in highschool. But the absence of evidence of effectiveness of the treatment does not imply that the treatment level should be increased.
I don't know of any research on this in a university setting. But there I support the use of homework for two reasons. The first is that there is much less classroom time. In school you spend over 35 hours/week in the classroom. At university a full load might be 15 hours a week. So practice needs to happen out of the classroom. The second reason is that university is supposed to teach skills around independent study. And the only way to practice that is to study stuff on your own.
I never did work in class. The environment was not conducive to being able to focus. It wasn't until I was away from school, at home, where I could actually think and work through problems.
You don't learn math by listening to a teacher explain it. You learn math by working through problems. That requires homework. You don't learn how to write by listening to a teacher talk about good writing. You learn how to write by writing essays out of class. You don't improve reading skills by listening to a teacher talk about a book. You learn by reading.
Maybe the claim is only concerned with younger children?