There is nothing in the Constitution that gives the Federal government any power over education. Which means according to the Tenth Amendment, the Federal government is specifically forbidden from any law, regulation, or funding of any form of education except maybe the military.
And since the Constitution is the supreme law of the land, Congress and the President can not change that. Think about that for just a bit.
Any Federal education law (and I do mean any) is illegal.
Any Federal education regulation is illegal.
Any Federal education funding is illegal.
Any. No exceptions.
Congress is specifically forbidden from doing anything with education. The Executive branch is specifically forbidden from doing anything with education. There is no Federal power over education.