As someone who was a child who was sent away to school by his parents, let me tell you that they matter a great deal. (Particularly from the POV of an adult looking back vs. the experiences of a child.) They are precisely the questions that should be asked to distinguish manipulations of "Think of the children!" hysteria and genuine issues of the human rights of minors.
Is there any answer to your questions that makes indentured servitude of minors acceptable?
Of course not. But I can imagine the level of state power and impingement on private family life needed to prevent that 100%, and that would be quite horrible as well. Government should regulate the conditions under which children are kept and raised by schools. However, the degree to which someone else should decide for parents what to do also needs to take into account the rights of parents and families.