So the system goes to jail if it doesn't enroll all school aged children? So the system decides which children go to public schools, charter schools, private schools, or homeschool? Of course not. At it's very core the responsibility for a child's education falls to the parents. Even if you send your kids off to school, you still need to be involved to motivate them, help them with assignments, etc. You can even see that the most influential factor in a child's success is whether or not the child has 2 parents (Harvard study).

Yes, you can take into account opportunity cost. However, that won't shift the responsibility, it's just the outsourcing of the labor. You can see this in any power structure (corporate, military, etc).