The problem with this strategy is that homework is mostly a tool for learning, not checking progress. Most teachers use homework as a way to get an extra hour or two of learning in each week for the students. If we remove it there will be less learning time available. So you’re gonna have to expand the school day or school year which means more teachers which is expensive.
If homework is not used to check progress, then cheating on it is not a problem.
Don't grade homework. Only grade work done in school. Students who cheat on their homework are just deterring themselves and won't do as good at the in-class, graded exams.
Well it comes down to what the point of school is. If the goal is just to figure out how competent a student is, sure, but if the goal is to educate students then reducing the amount of time they spend on school work will lead to worse outcomes.
