I think you’ve basically nailed it here. The goal is to make sure that poor kids get the bare minimum of education needed for them to toil. Higher education will be reserved for those who can afford private schools.

And my view is that it’s good for schools to teach a breadth of topic so that kids can get exposure to them and focus on the ones they find interesting. Giving students exposure to different aspects of math is useful, doing an in depth dive into these domains shouldn’t be forced.