A modest amount of public education protects against small scale market inefficiencies -- quacks selling poison, the illiterate being defrauded by their employers -- thus liberating a lot of spending power which is gobbled up by large scale, centralized market inefficiencies -- the myth of cancer treatment, the American college system, the legally sophisticated defrauding their employees.
There is no incentive for the really wealthy -- the people with the people's taxes, their work hours, their confidence -- to put money into education that would only make them harder to control.
Knowledge arises as a sort of after thought, and scholarship is a hobby; only in cases where the information asymmetry can be turned to advantage -- in religion, in technology, even in education itself -- does the scholar become a professional. Maybe the wise would be better off hiding their talent instead of making it available for institutional use?
I think it'd be great to privatize education but it still needs to be mandatory and free at a certain basic level.
My parents certainly weren't bad. Not that they ever did much beyond enrolling and sending me off to public school, but still. If public school wasn't there, I'm sure they wouldn't have left me completely illiterate. In fact I'm sure, and my parents now agree, I would likely have been 'better' schooled if it wasn't for public schools' near complete monopoly on funding and mindshare when and where I grew up.
None of the parents of people I know were 'bad' either, including those of many who insist on using mythical 'bad parents' as excuses for public education. Furthermore, amongst those I have asked, none of them seem to have acquaintances with bad parents, and I have asked enough people, from enough different backgrounds, to be convinced this 'bad parents test' could be applied recursively through all six degrees of separation without turning up more than, at most, some exceedingly rare corner cases. Rare as in at least an order of magnitude below likely available private charity to deal with them.
This doesn't mean I think everyone's parents are equally ambitious on their children's behalf, or equally concerned with educating their child; just that in absence of public schools, almost no parent would completely neglect facilitating any kind of education for their children, whatsoever.
The whole thing about evolution is that it never stops. However, evolution's definition of bad parents is brutally simple: those who have few descendants.