Point to a country that doesn't provide universal public education and I'll show you a country that lags the U.S. on every measure of standard of living -- economic opportunity, social equality, civic participation, personal freedoms, etc.
I do not contest that these are real benefits of universal education, and I do not contest that where this ideal has been approached (the Vatican is the only nation I'm aware of with 100% literacy) it has usually been by way of a government school system.
My objection is not event to government schools per se, provided that they are afforded adequate organizational, methodological, intellectual and ideological freedom.
The practical reality, however, is that the current American system has become crippled with restrictions upon how pedagogy is done which are stunting the benefitial effects that the system could potentially produce and has historically produced, leading to our comparative decline in most academic metrics when compared with much of the developed world. For example:
- The supplanting of a disciplinary model (your behavior must change to participate in society) with a therapeutic model (society must accomodate your illness/disability). Does any healthy, creative kid NOT have ADD/ADHD/etc? Do we seriously believe that the surge in such "conditions" has more to do with something different about "kids today" than it does with something different about "schools today"?
- The out-of-hand dismissal of any proposal which hints at "separate but equal" accomodations, in spite of demonstrable benefits for both separated parties (e.g., the British experiment with schooling boys and girls differently).
- The removal of proactive enculturation when it is tangential to religious issues (a teacher may be able to answer the question "what is Easter" in the manner you propose, but they certainly cannot present a unit on it in class, in spite of it being an important topic to understand for basic American cultural literacy).
- The removal of moral formation from the pedagogical agenda (How can you persue moral formation when you are prohibited (by fear of lawsuits and local policy if not by actual constitutional law) from endorsing or condemning any moral action/subject on which there is not near-absolute consensus? On what moral questions do we have even a majority agreement? Is such a least-common-denominator morality even worth teaching?)
- The lack of any epistemological humility when it comes to the presentation of "the scientific method" (the method itself is unfalsifiable in that it makes unfalsifiable assumptions about pragmatism equating with truth and a closed universe; its best "proof" is a self-referential "it works better than anything else we've tried").
- The "comparative religion" course which is (nominally) permissible will be rooted in a western, rational/evidentiary, secular textual-critical/historic-critical presentation of its subjects, that is to say, they are presented from the point-of-view of a particular theological/teleological/epistemological paradigm which may be at odds with the content of some or all of the covered religions, precluding an actual presentation of their substance.