That worked OK for the nation's need in the early 1800s. Then only a few percent of the population needed to be able to read, think independently, etc.
Most everything was done manually. For example, to walk behind a plow pulled by a horse or chop firewood etc. requires essentially no formal education.
In this century there is little need for unskilled (uneducated) labor and the nations the US competes with are growing faster mainly because they educate their population in math and sciences better than the US does. (While these subjects are useful in themselves, their main educational value for society is their development of rigorous and analytical thought capacity.)
If there were only private schools, then only parents would be paying for the general benefits that education confers upon the society. Only the relatively rich could give significant education to their children. Soon the nation would be forced to live with an elite leadership and unskilled masses - I.e. return to the life style of the early 1800s or that currently practiced by the "plain people" of Pennsylvania (no cars, TVs, tractors, etc.)
That is a sustainable life style and our petroleum based one is not so I am not strongly opposed to that way of life, but you must understand only that low tech manual labor life style is possible if only a few are well educated. Also as the Pennsylvania Dutch do, you must close your society off from the outside world.
I favor Federal funding of ALL primary education as the current local funding system, is causing many not to be educated to their potential in the US.
I.e. I favor NO private schools prior to college with equal educational opportunity for all. (Not good primary schools only in the neighborhoods of the wealthy.)
Using only a small part of the potential brain power available in the US is the main or fundamental reason why the US is losing its competition with others who do better job of educating their populations. We are trying to live in this century, not the early 1800s, yet have an educational system that is more suited to the life style of the early 1800s. One producing a well educated elite with most of the population poorly educated.
It is little wonder that US has world's highest crime and prison costs etc. The undereducated see what the elite has and find socially destructive ways to try to get the material goods the elite enjoys. Perhaps even more damaging to the US is that the masses cannot think for themselves and are easily manipulated by special interest groups and politicians. For example: Support the profit based health-care system instead one that delivers up to four years longer life expectancy at half the cost. Other examples in my old thread:
How Dumb can US Voters be? At:
http://www.sciforums.com/showpost.php?p=1689226&postcount=103
(It was made in failed effort to keep GWB from getting second term. The dumb voters will soon pay for their ignorance by living in the world's worst ever depression.)
Note that they are "dumb" is a result of the US education system - the fundamental root of the US's problems. For example lack of adequate education let selfish, commission-hungry, bankers etc. sell them houses they could not afford, etc. and made the present economic collapse.