Homework in math in particular does show a pretty useful jump in the post-Algebra I period.
This I believe. I don't know why it's the case, but I'm going to hypothesize that homework helps with higher-level subjects because succeeding in them requires the development abstract thinking skills (assuming that the course hasn't been watered down).
Also, I'm thinking that these classes move frequently to ideas that are conceptually very different compared to math courses in primary school, which tend to focus on ideas that are the same or conceptually related. Lower-grade math classes also seem to go over last year's stuff until November-ish, as well (at least around here).
