Retrieval practice and attempting to solve problems before you know the solution to them _does_ improve retention [1]. At least in my high school, those drills definitely exercised these two ideas. In college I copied half my homeworks from answers or exercised the option to make my grade entirely dependent on exams and I definitely retained less information than if I had done the homework.
That's the real problem with the studies saying homework does nothing. Drill does improve learning! But that's not showing up in these studies for some reason...
drill improve short term memorization! But unless the exam are focused on memorization instead of on understanding and mastery this will not make a significant impact on exams score.
[1]: https://www.retrievalpractice.org/make-it-stick