It's true that children have fractional rights in our society, and that's probably a good thing. But your other questions are like, "Do we have proof that beating/drugging/indoctrinating a child is bad for them?" We simply should not experiment on children. Full Stop. If we would not allow ourselves to be treated in this manner, then we shouldn't treat other human beings that way. Especially those who, because of their undeveloped state, have less rights than us. The situation is unnatural and repressive, and proof of damage is not needed to stop it, proof of harmlessness and benefit is needed to continue it.
To your question of jails, no one ever said it worked perfectly, and recently, many schools have given up on even trying to instill a love of order. Instead they have been raising rioters. And it is certainly working. I could (and I have in the past) written whole posts on why State School "socialization" is the last thing children need.
RE: For those who still think State Schools are about education