That's not how the real world works, only an idealized one. And not all public or private schools are the same. In the US, private schools were motivated (but n

That's not how the real world works, only an idealized one. And not all public or private schools are the same. In the US, private schools were motivated (but not forced) to adopt better approaches because they were often competing with widely-available free public schools. Some public schools were being ruined by inept education bureaucrats, so wealthier parents moved their kids into better private ones. This is because some states and school districts were overriding the wishes of the parents, so the said wealthier ones did was was easiest: change schools. This created a two-tiered system in some areas where public schools got worse because they lost money per student as students left, had to cut budgets and good teachers, and concentrated poor and inner city students within underfunded, failing school districts. There are good public schools in some areas and there are probably plenty of horrible private schools too. It's my experience in the US that the best private schools tend to be better than the best public schools because of the extreme differences in resources.