First, there is the economic argument. We need to help people acquire the skills to make a living, so they will not become a burden upon their neighbors. Toward that end, the '3 Rs' approach showed what was important for future workers at the elementary level; at the secondary level, many youth not destined for learned professions left before graduation to finish their schooling in apprenticeship programs or to work on the family farm.
Second, there is the citizenship argument. A democracy requires voters who understand how their government works, the history of their country, a sense of what is going on in the world, etc. That way, they will be able to make intelligent choices at the polls, be not easily swayed by demogogues, assist in local government.
And that's it, folks. Nothing in our original vision of state-sponsored education foresaw physical education, school sports, cheerleading, band, and a gazillion other things we think we can't do without. Public schools were pretty minimal in their approach. Today, insofar as the bells and whistles we all like distract from the basics of preparing people for labor and participation in democracy, those bells and whistles can and should be curtailed.
The case is different for higher education. Colleges and universities have a history older than our Republic. Yet we have added something to the mix.
What we inherited was the idea that scholars are useful to have around. Government shelters learned societies (including colleges) because they produce learned professionals and new discoveries which benefit society -- and because they are an ornament to the government which endows their more, uh, speculative endeavors. But you never know what the scholar will produce, only that he will produce something. So you make it easy for scholars to associate, and await results. This is the whole raison d'etre of the medieval University, and it is as valid today as it was in the 13th Century.
What we added to the mix was the idea of colleges which would do research that would benefit the State directly, as in land grant colleges researching and teaching new agricultural techniques. This idea has worked its way outward in all directions. People may gripe about big universities being more interested in research than in teaching, but this is a recognized function of the big State school.
The question remains, though, what right or wisdom there is in letting government interfere with this goose that lays (we hope) golden eggs. At the elementary and secondary level, I would say that the State has an extensive right -- and need -- to interfere.
Bad teachers are the fault and responsibility of the teaching profession. As with any learned or skilled group, teachers set the standards for their colleagues -- and rightly so. They have this in common with both doctors and plumbers. What they also have in common with the other learned or skilled groups of workers is a reluctance to crack down on obvious incompetents. We got 'em in the clergy, too, and unless they do something morally outrageous, it's next to impossible to get rid of 'em.
Bad teaching, on the other hand, is defrauding the government. After all, the government has a right to supervise the workers it contracts with for services. A construction firm must meet deadlines or default on its bond; its materials must meet standards for content (so much sand in the cement, not over so much . . .); its handling of money is open to audit -- all this just to build a bridge or a road. A school should be open to the same review. The government contracts with the school and its teachers to provide a certain education to our children. Government must be allowed to specify what they want to see accomplished (esp. as regards the two reasons gov't operates schools, above), and there must be penalties for those who fail to provide it.
At the higher education level, the interest of the government is different. Government should not meddle in what learned societies do. Academic freedom is not a sacred right, but it is wise policy. Government only screws things up when it tries to meddle with it. This does not mean that universities or professors should be subsidized in seditious activities; and public institutions should not interfere with normal government access (like military recruitment), simply because the State owns the place. But getting in a squabble with a bunch of academics is time and money wasted.
On the other hand, the second thing government expects out of higher education -- the R & D function -- is another government contract, like any contract, and government has a right to oversee how it's spending its money. Likewise, any school that accepts government money accepts the strings that come with government funding.
We have put up with degreed dullards awarding themselves tenure for too long. I think the government is being defrauded by its schools, and I think heads need to roll. A new model is required for public schools, but it will not come from the teaching profession and its allies; it must be imposed from without by a government whose citizens are tired of being ripped off.