Uh, it's not like "problem kids" are necessarily getting a good deal from the public system. Special ed kids are forced to learn "academic" style knowledge rather than the practical life skills they actually need... and behavior problem kids use way more resources than they deserve and harm all the other kids in the process.
Sadly, many kids in special ed programs and many behavior problem kids would not have problems in a different type of learning scenario... but the entrenched K-12 classroom, 30 students one teacher, hour long periods, boring books, exercises, silence, etc., is just a horrible fit for them.
You completely missed the point. Comparing a single private school, or some subset of them, which has selective admittance with public schools which have to educate everyone is not sound.
Sadly, many kids in special ed programs and many behavior problem kids would not have problems in a different type of learning scenario... but the entrenched K-12 classroom, 30 students one teacher, hour long periods, boring books, exercises, silence, etc., is just a horrible fit for them.