We already fund a significant portion of schools federally, even if the majority of funding is local. An argument can be made that education can be considered interstate commerce since people can move at any time and take their education with them.

That said, when I took my first semester at a state university in the 90s it was able to be paid with a summer job working minimum wage while my parents paid for the dorm. Four years prior I could have paid for the dorm and the entire year with the same summer job, but university costs had doubled in four years because the state funding was cut and they shifted the costs onto the students. It has only gotten worse since.