> You don't think there will be small schools who want to take them?

Spending a second of logic on it and thinking critically, there won't. Why would a school empowered to be choosy and subject to profit motivations choose the pricier students to specialize that reduce their rankings?

And why do you think a flood of schools arguing germ theory is a lie be a public good?

I went to religious private school and too had teachers who taught some bullshit things. Dinosaurs were fakes buried in the soil by the devil to test believers. Evolution is a lie by the government. And yet by personal experience I'm more learned than the average public school peer I know. I'm a somewhat special person though; I know many in my class that still believe without question. It's not a good thing for society overall to have such "knowledge".

As for why kids wouldn't be able to leave the public schools, some schools will be required to provide transportation. Others won't. Some will be able to be choosy, some won't. You see where this goes? Those schools which are choosey and don't provide transportation will end up selecting the most well off while those unable to be choosy and/or forced to provide transportation will be forced to shoulder those who aren't good performers who don't get into the choosy schools with a transit scholarship.

You are ignoring the externalities. We end up with an ignorant society that ultimately harms all of us. I hate to use a movie trope here, but we're barely a step above Idiocracy when it comes to the ability of the average American to function and make decisions. This ultimately becomes self destructive.

I went to a young earth creationist Christian school and it messed me up. Most of us had a hard time adjusting to life outside the Evangelical Christian bubble. It's really hard to connect to others when your identity is tied up in believing a lot of outlandish things and it's hard to love yourself because you're given a long list of crazy rules to follow. I was told that kissing someone before I was married would taint my soul and whoever I married would be disgusted by me if I did so. Most people I've kept in touch with regret going to that school and every queer person I know has been absolutely traumatized by the experience. I'm happy, and by your criteria, a good member of society but that was despite my school. It took a lot of therapy, personal growth, and finding a community of people who actually care about me to be happy.