Why not? Public schools have a long history in this country, with even Thomas Jefferson being a proponent. The Land Ordinance of 1785 specified one acre for a public school in each township, and about half of the founding states had public education in their constitutions.
Education being best managed locally, our problems began when the states started exerting more control over districts and combining them for easier top-down management. Then the federal government got involved, making things even worse.
I started school in 1942 and watched the transformation, Schools started to consolidate in my area in 43,44, but the big change came about as community schools were closed and moved to the bigger and better facilities.
My school had 3 classrooms one Principal(War Vet) his wife and one other teacher. Principals were always classroom teachers in the smaller schools.
Standards for Math and Science began to drop down in early 50's, but the ultimate destruction came under Carter. Pl 94142 and then the Federal Department of Education, finished the job.
Schools in Middle America were not dominated by Marxist, anti Christian zealots as they are today.