The core issue of this public policy debate is not about money. It's about competing visions over who has the right and responsibility for the education and upbringing of children.
The rationale animating the creation of the US Department of Education is that government knows best. Consider the remarks of Congressman Samuel Moulton of Illinois one year before the US Department of Education was originally established back in 1867. The department would be:
...a pure fountain from which a pure stream can be poured upon all the States. We want a controlling head by which the conflicting systems in the different States can be harmonized, by which there can be uniformity. ...I take the high ground that every child [is] entitled to an education at the hands of somebody, and that this ought not be left to the caprice of individuals or [the] States so far as we have any power to regulate it." (Remarks made on June 8, 1866, pp. 3044-45)