I suppose my concern is that, while public schools may promote democratic citizenhood, they are less likely to induce good republican citizenhood (using "democratic" and "republican" in the sense of governmental models, not in the sense of donkeys and elephants).
Looking at the government of the US from the perspective of the framers, a liberal (protecting the liberties of people) society is preserved by a parliamentary republic which is sufficiently conservative (slow and hesitant to act or intervene). Such a legislature can be realized by having many factions represented (the more the merrier), producing gridlock and all flavors of legislative logjams as safeguards to keep the government from being able to do much of anything (read: "being able to step on too many people's rights") without truly broad-based support. Indeed, the reduction of much of US federal politics to two-party scuffles is itself problematic to this model, but that's another node.
I postulate that a state-run school system such as that in the US, particularly when constrained by current jurisprudence, is inamicable to a healthily factionalized populace. Rather than encouraging a diversity of epistemologies, it teaches and allows for only that subset which is naturalistic and positivistic (after all, one allowing for authoritative revelatory knowledge could necessitate a supernatural/transnatural authoritative revealer, much as special creation demands some flavor of creator; this raises First Amendment issues). Rather than encouraging a diversity of worldviews, children are largely indoctrinated using the majority cultural orthodoxy of the time (which is a polite label for political correctness; consider emphases upon "tolerance" as an intrinsic virtue without respect to the object of tolerance). The philosophical and political goals of the NEA (that is, a particular union's majority orthodoxy) can also find their way into standardized curricula (e.g., the outcome based education debate) or "acceptable" practices (the line between corporal punishment and abuse). Even the practice of holidays is problematic; how do you initiate a child into a culture which widely practices Christmas (or even worse, Easter) when speaking about Christ in any sense except as an object of historic textual criticism is verboten?
Taken over the long term, such constrictions cannot help but diminish the mindshare held by dissenting opinions (quite apart from their pragmatic, legal, and rational strengths), thus de-factionalizing (homogenizing) the population and diminishing the protective value of an adversarial republican government.