To see the big picture of "state" education, legal facts must be squared with the facts around laws. It's a fact that Utah law recognizes the parent as the main player in a child's education. It's also a fact that the number of educated children rose with compulsory attendance.
We want both liberty and literacy, or the best ratio. But I question whether liberty has been meaningfully infringed by compulsory attendance. Are there droves of parents who are fined for taking their child on vacation, or because their child is ill? Are the forms for home-schooling so arcane that the Libertarians are on alert? Why are core standards a concern for basic understanding considered constrictive? (Does it all come back to sex and the theory of evolution?)
A third fact: My parents were not the main players in my education. Certainly, my parents instructed me morally, but in algebra they were secondary and supportive. And I suspect this is true for the majority of American children.