Yes, we do.
To repeat: the arguments for parent control of education parallel the arguments for markets (the system of title and contract law). The system of title (State recognition of a right to control a resource that includes the authority to transfer the resource on terms mutually agreeable to the donor and recipient) and contract law unites local knowledge with the incentive to use resources in socially beneficial ways.
If you wish to use this analogy fne, but i do not think that the provision of education services mirrors a market with property rights and contract law.
First, lets look at contract law. At its most basic a contract is an agreement between two or more parties where goods and/or services are given in exchange for a consideration. The parties are required to enter into these arrangements without duress, and in understanding of their rights and obligations under the contract. Children due to their lack of experience, and knowledge are deemed to be incapable of entering into most contracts (simple purchase agreements such as buying food stuffs are exempt). Therefore any contract whereby an education is provided to a child cannot be entered into by the child itself, and a legal adult is required to therefore exercise their judgement on behalf of the child. And the child, beign considered incapable in the eyes of the legal system, is unable to register any opposition to the contract - imposing a considerable amount of parental compulsion on the child regardless of what that parent's choice is.
Policies that give to parents the power to determine for their own children how those children will spend the time between birth and adulthood empower people who know individual children best and who are most reliably concerned for their welfare.
This would appear to be the situation in the world at this point. Looking at the province of Ontario, a parent/guardian acting on behalf of their children can:
a. Send them to the local school (with options for the Public board, Catholic board, French Public or French Catholic board);
b. Send them to a school that is not local (ie "out of district") if certain criteria are met;
c. Send them to a private school;
d. Home school.
As the schools at option a. are publically funded through taxes (both those collected by the municipality and the province) people don't need to worry about coming up with additional funds for schooling.
Those options apepar to exist in most other jurisdictions on this planet.
Furthermore, policies that give to parents the power to determine for their own children how their children will spend the time between birth and adulthood create incentives for providers of education services that differ systematically from the incentives in a State-monopoly environment.
As there does not appear to be a monopoly on the delivery of education to children, your point wrt the lack of incentives in a monopoly system is irrelevant.
To be sure, some children will fall through the cracks in any system.
Any system where the costs of education are solely borne by the parents of children will cause a much larger percentage to "fall through the cracks" than one where the costs are spread across the entire tax base. As I showed earlier, the average costs of a year's education for primary and secondary education in Canada is approximately $11,000/student in the publically funded system. Private schools appear to cost about $13,000/year.
As an anecdote, if I was to have to defray the entire costs of my three children's education personally, it would consume approximately half of my annual income. Given the rather harsh physical and economic realities we all face, that would likely cause me to have to pick which one gets the formal education that will permit the opportunity for something other than menial employment.
By spreading the costs of education arcross the entire tax base, it allows all children the opportunity to receive an education, preparing them not only for employment, but also preparing them to operate in the wider society. Little things like having to wait turns, listen to authority figures (because unless you are very exceptional, you will have a boss or supervisor at some point in your life), and how to get along with your peers.
Jose Padilla attended government schools. John Walker Lind attended government schools.
Nice poisoning of the well - however:
Mr. Lindh got his high school equivalency diploma at a school offering self directed studies and was able to leave that school system at 16 (isn't that something you approve of?) and then went off to further his education overseas at a variety of religious schools before getting yet more education in paramilitary skills (presumably he needed to pay to attend the madrassa)
Mr. Lindh would fit the educational mold you have advocated - self directed studies based on the interests and ability of the learner, a standardized test to be taken at the appropriate time and additional OJT to round off the skill set.
If it is your intent to argue that government schools are responsible for the likes of Lindh and Padilla (and I seem to be drawing a blank on where he received his education), can I point out that Vlad Tepes Dracula, Ivan Grozny, and others were educated by private tutors. Your observation is rather pointless.