People get the wrong ideas about federal departments. The department is only allowed to do what is mandated by the congress. Local school districts decide curriculum, which text book series to be use, how much technology is to be provided, etc. The Department of Education administers federal programs aimed at helping special needs children, early morning and after school day care, federal subsidies for schools, various miscellaneous programs and supposedly sets a broad agenda for local school boards to follow. The department was involved in the bussing issue of years past and other similar things.
The effectiveness of a public school system is determined and must be decided at the local level. It is there where schools are decided to be built. It is there where teachers are hired and fired. It is there where public input plays a roll.
Is the Federal Department of Eduction, efficient? Probably not. It can be made better, but it probably does provide some benefits and some level of continuity among the states.