This suggestion is highly inconsistent with the data from the article.
Every nation out-performing the United States has a strong and well-funded public school system. Although some have a hybrid model, the hybrid models favor public schools over private schools. And hybrid models hardly constitute "abolishing".
There is also a strong correlation between states (in the US) with high per-pupil spending and states which out-perform the US average [1].
> but every segment of the population will be catered to by price, taste and other preferences.
"Same quality, lower price"? Extraordinary claims require extraordinary evidence.
[1] I am comparing Fig. 1 of the article with the table titled "Current Spending per Pupil" on this page: http://www.governing.com/gov-data/education-data/state-educa...