The reason why federal aide was allowed the colleges but not the schools was the specious distinction between a school and a college. Schools are for indoctrination, but colleges, not. But the GIs who went to college on the GI Bill often remarked how childish were the 21 years olds they found themselves in school with. High schools are for indoctrination only if they become no more than higher elementary schools, holding pens to keep boy and girls from growing up.
We used to joke that college was just H.S. with ash trays.
(then they banned smoking)