Hardly? What do you mean? Paraphrasing and re-paraphrasing the Soviet Union’s Constitution’s line about how “the church (should be) separated from the state and the school from the church” is “hardly” an affirmation of big government?
The Founding Fathers certainly did imagine the possibility of centrally-controlled mass education given the history of the Old World with such limiting systems, which is why they did not set up the federal government to contain such instruments.
Neither the US Constitution, nor the Federalist Papers, nor other documents related to our Founding contain discussions of Federally controlled mass education.
The reason, as you would agree, is that they neither imagined nor supported such ideas.
And that is certainly an argument for abolishing the US Department of Education, plus all other Federally directed interference in state & local school systems.
However, the fact remains that we now do have, and have long had, mass public tax-payer supported government-education controlled, ultimately, by the Feds.
This system has been tested in courts many times, which have refused to rule it unconstitutional.
Further, even allegedly "conservative" Republicans -- Governor Perry comes to mind -- are afraid to say they will abolish it, if elected.
So government-schools are ruled by interpretations of the Constitution which prohibit "establishment of religion" and define the word "science" as natural-science.
Given all that, I argue that you don't want government-teachers teaching religious doctrines to your children.
What you want instead is that those people stick to their subjects -- i.e., math, English, science -- and leave the teaching of religion to qualified clergy in voluntary religion classes.
How can you even possibly disagree with that?