Probably because it is in violation of the 10th Amendment/Reserved Powers clause. The constitution does not give the Federal government authority over education in any way whatsoever. It is the principle of a limited national government. If you give it in this case, where do you draw the line?
As a public school teacher, I DESPISE the dept. of ed. I cannot think of a single positive impact they have had. What I understand, is that this was pushed by the NEA in the 1970's...a very socialist perspective at that. Very similar to Hillary Clinton's whole "it takes a village" concept. Collectivism at its finest. They wanted to take kids at the age of about 2 and take care of "all their needs", basically socializing them into adulthood.
I can only speak of Texas, but it is also dreadful to see the damage our State governments have inflicted. Unfortunately, this is an issue that people care about in the weeks before and election but to which nobody pays attention. We are talking about an extremely watered-down curriculum, making excuses for kids wherever we can, etc.
Education is to be done at the LOCAL level and that level only. The so-called "independent school districts" we have today are a total joke and nothing more than an appendage of the state/federal machine.