In a nutshell, you’re suggesting that it’s unconstitutional to implement structures that require taxpayers to federally fund post secondary tuition. The mere existence of tuition grants for post-secondary education at the federal level, and the conspicuous absence of successful constitutional challenges in that area, suggest that constitutional law scholars do not share your opinion.
I'm not just suggesting it, I'm blatantly asserting it. Our federal government has become so bloated with over reach we have become blind to it. The lack of a challenge does not equate to a reality. Have you ever heard of the story of the Emperor's new cloths? Existence also does not equate to correctness.
Once again, please find me in our Constitution or it's amendments where education, and especially post secondary education is outlined as a duty / purpose / responsibility of the federal government and then we have a different discussion. You can't, it's not there.