The Education Department wasn't created for a real need. Upon signing its creation into law, Carter said:
"Primary responsibility for education should rest with those States, localities, and private institutions that have made our Nation's educational system the best in the world, but the Federal Government has for too long failed to play its own supporting role in education as effectively as it could. Instead of assisting school officials at the local level, it has too often added to their burden."
With that being said, it defies logic that the creation of an immense new bureaucracy would "ease the burden" of assisting schools at the local level. This was about power and the potential to control the curriculum agendas, and whichever ideologies could be taught in all 50 states. With federal tax money to the schools come conditions and strings.
Public school systems existed before it's creation and would continue to exist if it were abolished.