Pointing out that a bias exists is not always a call to eliminate that bias. The fact that merely requiring an application rather than being the default option improves average outcomes isn't a problem that needs to be solved. It's just something that should be kept in mind when comparing schools.

Right.

At some point, some school is going to have to take the kids who don’t bother applying, since we can’t put 100% of schools behind an application and preserve its benefits, and we should not be surprised that such schools do worse, if the ones who do apply happen to be better.

I don't propose anything. I'm just pointing out that the point that kicked off this line applies to charter schools too.

I get a feeling the only way a school can satisfy your standard for "not cherry picking" are those armed with Omnipotence

What part of the original “being able to kick students out” are you claiming is happening here?