The case for the Department of Education could rest on one or more of three legs: its constitutional appropriateness, the existence of serious problems in education that could be solved only at the federal level, and/or its track record since it came into being. Let us consider these in order.
(1) Is the Department of Education constitutional?
At the time the Constitution was written, education was not even considered a function of local government, let alone the federal government. But the shakiness of the Department of Education’s constitutionality goes beyond that. Article 1, Section 8 of the Constitution enumerates the things over which Congress has the power to legislate. Not only does the list not include education, there is no plausible rationale for squeezing education in under the commerce clause. I’m sure the Supreme Court found a rationale, but it cannot have been plausible.
On a more philosophical level, the framers of America’s limited government had a broad allegiance to what Catholics call the principle of subsidiarity. In the secular world, the principle of subsidiarity means that local government should do only those things that individuals cannot do for themselves, state government should do only those things that local governments cannot do, and the federal government should do only those things that the individual states cannot do. Education is something that individuals acting alone and cooperatively can do, let alone something local or state governments can do.