For those exceptional children and circumstances, I agree that a greater amount of flexibility would likely be beneficial. However, you appear to be arguing that this approach should be extended to all children and parents, replacing the existing structure of formalized K-12 public schooling....we return to this question.
The argument does not proceed from exceptional cases to a generalization. I use exceptional cases as stark illustrations of the generalization.
Back up several steps.
The government of a locality is the largest dealer in interpersonal violence in that locality (definition). Place industries on a continuum. What part of the continuum from "very likely candidate for State operation" to "very unlikely candidate for State operation" does the education industry occupy? In abstract, the education industry is a very unlikely candidate for State (government, generally) operation.
Why does the State intervene in the education industry at all? This "why?" question has three interpretations: 1) The welfare-economic "why?". What does society gain from a State role in the education industry? 2) The historical "why?". What events coincided with the State's entry into the education business? 3) The political science "why?". What do those politicians who support the State's presence in the education industry gain from their support?
1) See below.
2) Anti-Catholic bigotry.
3) Dedicated lobbying by current recipients of the taxpayers' $500 billion+ per year K-12 education subsidy.
1) We consider the welfare-economic argument for a State role in the education industry here.
The case for subsidy is weak. Given the case for State subsidization of the education industry, the case for State operation of schools for the general population is weaker still.
Please read the introductory section (p 88) in West, E.G.,
Education Vouchers in Principle and Practice: A Survey
The World Bank Research Observer, V12, #1, Feb., 1997.
The education industry is not a natural monopoly. Beyond a very low level, there are no economies of scale at the delivery end of the education business as it currently operates. "Natural monopoly" and "economies of scale" are the usual welfare-economic arguments for State operation of an industry. Even when an industry qualifies as a natural monopoly or exhibits significant economies of scale the case for State operation of an industry is not decisive, and the education industry is not a natural monopoly and, beyond a very low level, does not exhibit significant economies of scale at the delivery end as it currently operates.
Education only marginally qualifies as a public good as economists use the term and the public goods argument implies subsidy and regulation, at most, not State operation of an industry. The State cannot subsidize education without a definition of "education" but then students, parents, and real classroom teachers are bound by the State's definition. You will have a hard time finding a definition specific enough to guide a bureaucrat whose job it is to assess whether State funds are well spent and yet general enough to encompass all that normal people would call "education". In consequence, policy makers compose restricted definitions which force wildly varying children into a narrow mold. The results are tragic.
Further, State assumption of responsibility for the provision (even through subsidization) of public goods does not eliminate the "free rider" problem at the root of "public goods" analysis. The State is a corporation. Corporate oversight is a public good. Oversight of State functions is a public good which the State itself cannot provide.
I see a semi-plausible case for State operation of schools for some limited subset of the sub-adult population. Compulsory attendance statutes mean little unless some schools must accept students rejected everywhere else. Call these default-option schools "the public schools". Taxpayers do not benefit from policies which give a narrow cartel (the NEA/AFT/AFSCME cartel) a long-term exclusive position in receipt of the budget dedicated to the operation of these schools. Taxpayers would benefit from a policy which periodically put contracts for the operation of these schools out to bid. Let the NEA compete with the HGEA, the AFT, Edison, The University of Phoenix, and the Catholic Church for these contracts.
Government is not some all-seeing, benevolent God. People do not become more intelligent, more altruistic, better-informed, or more capable (except in their enhanced access to the tools of violence) when they enter the State's employ. Children are not standard. Remote State actors, wielding the blunt instrument of State violence, have little usefully to contribute to the education industry.