If there's a social interest in education, it is that it be universal. Government of the people by the people necessitates a literate electorate aware of and able to uphold its liberties and responsibilities. Therefore, we may suppose that universal education is a general good and therefore necessary and proper.
However, seeing that everyone possible receive a basic education is as simple as spreading around some money. It's utter overkill for government to own most of the schools, employ most of the teachers, dictate the curricula, and ban certain books from classrooms and school libraries.
Besides, immersing children in a government organ for twelve years from the formative age of five hardly conditions them to become adults that look down on government and see it as a limited, servile institution bolted onto the side of an independent society. On the contrary, such immersion conditions all too many to look up to government for food, shelter and marching orders.
There many constructive ideas circulating for improving curricula or presentation style. However, the complexity of most suggestions illustrates a strategic weakness of even having a public school system: it has drawn all of the tactical and economic decision making into political processes, which imposes a one-size-fits-nobody monopoly on 90+% of the students in the country.
We could dispense with all of that simply by privatizing K-12 education. Government can achieve society's general goal of universal education merely by paying for it; it is unnecessary (and very undesirable) for government to own the means of production, employ all of the labor, and micromanage them through an elaborate, self-serving bureaucracy (hey, isn't that the embodiment of socialism?).
Let's let profit-seeking entrepreneurs compete for scholarship dollars without a prepaid service (however inferior) stacked against them. They'll try all current classroom suggestions and more, and those yielding the most perceived benefit per dollar will proliferate through profitability. Education can evolve via economic Darwinism, just don't call it that in front of school-voucher creationists.
What's more, private schools will be diverse, not uniform, so that more families can find what they want, so that they won't be energized to try to impose their idiosyncrasies on a system shared by nearly everyone else. Education can be universal, but should not be uniform. We are supposed to be cultivating a free society, not regimenting an obedient army, the original aim of the Prussian system after which ours was modeled.
For the American economy, I don't think that anybody can predict that. When was the last time private education in America operated without competition from prepaid public? 1830? Our economy has grown a bit since then. Information technologies have improved somewhat too. In the mean time, outside of church subsidized schools, only America's wealthiest have been able to afford to walk away from whatever tax-paid inculcation the state was dishing out, whether it was the overtly Protestant curriculum of the past or the PC curriculum of the present.
With America's current prosperity and information technology, if we rescinded the taxes that pay for education, we might actually be able to achieve universal education with little or no government assistance. That doesn't mean that I want to experiment (I don't), but I can wave off criticisms of free markets that are based on conditions almost two centuries in the past.
Could a few TV channels deliver the knowledge? Could tests disguised as games measure mastery? We just can't know; we don't have many modern reference points. However, I do know that a whole lot of kids know an awful lot about Pokemon creatures, and the government didn't have to pay for any of it. That learning could have been about real animals and plants, or people in history, or any of a number of things that schools would teach. That proves that a free market can distribute information to kids without government assistance. Our obstacle seems to be motivation, not wealth.
First, the question assumes that universal education requires schools and tuition. I can't find anyone who can tell me why we must have schools in the sense of having expensive buildings and teachers. See Innovation. However, if we must have formal schools, and if some families can't afford tuition, then the government can help people to afford them without owning or operating them. Just as with food and shelter and college, government can distribute money (or forgive some taxes) and leave the rest to free citizens.
Government operation goes way beyond making education universal. It tends to make education uniform. It's just the way bureaucracies are. There's usually just one bureaucracy for any task in any jurisdiction, so there is usually just one brand of whatever that bureaucracy does. Even worse, government bureaucracies tend to be immune from competition and bankruptcy, so their offerings can be very bland.
We don't need uniformity, especially in a free society. Uniformity is a characteristic of authoritarian societies. If it emerges from the choices of individuals, then that's okay, but if government is driving it, then we should suspect social engineering. Even if well meaning politicians didn't have social engineering in mind when they created it, a monolithic education bureaucracy attracts ideologues like flies. There's something about modulating the message being delivered to a captive audience of young, uncritical minds that appeals to ideologues of all stripes from both the right and the left. I wonder why.
Oh please! Do grocery stores open up in rural America? Urban America? What's so special about education that it wouldn't follow suit? Could it be the interference and competition from the socialized schools?
Don't get stuck in the big-government-school mind set. Schools don't need to be giant campuses with thousands of students trucked in by a fleet of buses. They also might not need to stratify students into the grades that most of us grew up with. The one-room schoolhouse of the past may yet be the wave of the future... I don't know, and I don't need to know.
The nice thing about free market economics is that neither I nor any bureaucrat needs to design a complete operational solution. Provided modest resources and left free, private enterprises can and will attempt many operational plans, and the most economical will proliferate while others vanish... and do so much more rapidly than any politicized bureaucracy could or would ever adapt.
All we need to remember is that the people who live in various places are better qualified to solve their own problems than distant ivory tower academics who would impose one ignorant solution on many diverse subcultures.