Private schools CAN compete with price
How so ? private schools can't force people to pay and then say "it is free, education is priceless !". Only public school can do that.
The fact that private schools are costly is just because they can't compete on cheap price with the public school system.
A second reason is regulatory walls (or loan backed by government for 'the approved ones') that keep outsiders from competing with established players.
Private schools can charge whatever they want. That is why they are expensive. The operating costs of a private school are identical to a public school of the same size and activities. Given these constants, the differences in price are made up by salaries, social parameters (exclusivity, religious teaching, special treatments, etc.) and socioeconomic demographics of the families that attend. Taxpayers pay for public schools to exist. The Gov't doesn't dole out extra cash making public schools able to exist better than private schools. The difference between public and private education is that generally private education is for profit. Public schools will always exist given the Gov't mandates compulsory education to a minimum grade level.
Without public school system, the poor would still demand education and, as a consequences, the supply will always come.
The supply does not have to come from the rich, poors have brains, hands, and ambitions if you let them work and earn their living.
This is very true, however; it is not in the ruling party's interest to let the poor do this. Many argue that the poor are not worthy of having an education because they are poor (and why should they be supported if they can't themselves). This is a deep fundamental question in all societies. Education is treated this way in the US. It is a means to separate people. Many complain that the regular average joe who is hardworking can't afford a public school college education valued at ~$30K, yet they have a nice new Prius in their driveway. I am not arguing one way or another, but if you give people options instead of telling them what to do (on some things like education), history shows people are very short-term driven with poor ability to see the benefit in things outside of "what every else has." There will always be poor(er) people than others. Does this mean they don't deserve certain things?
Of course, funding from the Gov't for education (the US) is done mostly by headcount. The public sector of education has far more students than the private ones. It's like the difference between running a company like Google and running a small mom and pop grocery store. The public sector of education is so large, it makes it easy for money to be utilized poorly. The Gov't funds education by throwing money at it with no target or outcome desired. It just does it. The Gov't does this because: IMO, Americans don't really care about becoming smarter or educated. It is all profit driven. More education = more money. That's it.
A capitalistic approach (the US) to education results in an education gap that favors those with money gaining access to knowledge over those who cannot afford it
Saying at a time where virtually every book on earth can be read for free. (tip: and it is not thanks to the help of the public sector)
You can now see the model changing for higher education (college). It is because of the public sector. States are no longer funding public colleges at the level they used to. This has strained colleges and in turn, they extend that strain onto incoming students in the form of higher tuition. It is to the point where a public college costs nearly as much as a private one. This is why people are pushing to put things online for free. Learning should not bankrupt people. It should be widely accessible, low cost and supported (if a country wants to remain competitive and adaptive with a bright people).
Education has a price. If government spend budget X for Y children, then it cost X/Y per children. Competition drive the ratio X/Y down.When one says "something has no price", he forgets that a human somewhere lost precious hours of his limited time on earth to pay the price. "Having no price" put no limit on how much people will be sacrificed to keep a dysfunctional system working. If you are glad to be that person, good for you. I won't be.
The illusion you're buying into is that somehow if you can vote with your dollar, your child will get "a better education" at a private school if everything were not mandatory. The value people place on education for the learning sake is broken. If I told you that paying for college would not get you a higher paying job (on average) in the future would you go? All things constant, if education were optional and that learning was not important to make money, would you still pay for it?
People in America go to college for the wrong reasons. You go to learn. To think. To develop thoughts about the World. Public school (K - 12th grade) teaches kids the basics of existing in a society (basic maths, personal finance, how to read, write). This NEEDS to be compulsory. These skills are a basic requirement of living in a society. See history for millions of examples of why this is important.