To an extend yes. Absolutely true up to and including high school, but at some point diminishing returns kick in.

The idea that all education at any cost carries positive externalities is exactly what got us into the mess that is education today.

Edited to add: Also, my proposal isn't incompatible with neither financial aid nor grants to institutions. But like underpriced mortgages caused a housing bubble, underpriced student loans is causing an education bubble.