We pay for primary and secondary education through the public till for the following reasons:
1) Most state constitutions require it.
2) The return on the money invested in primary and secondary education for children of parents who care about their children's education is enormous.
The return on money invested in most public consumable health care has almost no return. The fact that you make a comparison between those two public functions demonstrates the sort of education that your parents gave you.
A special note is that primary and secondary education is paid for by state and local governments, and is under the control of the local authorities that represent the people who are consuming and paying for the service. Obamacare: not so much.