You are assuming a world where parents are guided by reason and data.
“Different students respond in different ways to different educational environments”
But then again to gauge how individuals respond to an environment it must be clear that said environment is an option, that they have reasonable resources to prepare for it. A rich parent may provide 1000 books for their kids, but can’t make them read. But it’s already an advantage. Access to schools isn’t just the affordability of attendance but also access to the opportunity in the first place.
One way or another there must be more ways to level the field.