Joseph, if families would save the money from homeschooling their younger children, then they would be able to more afford tuition for older children.
In addition, they could hire a tutor (lets say a Kollel guy) to devote a few hours a day. That would be significantly cheaper than paying a regular school and the older children would still be learning (as would the kollel guy). As for chemistry and other harder subjects, they could either hire a tutor, find someone competent in the community or find another creative solution.
If both parents are working, this is obviously even harder.
We cannot maintain a system that relies on too few to help too many. And that is what the current system seems like to me. Can Hashem provide money at any point? Sure, but relying on that is neglecting your hishtadlut.