The fact that we have government schools prove differently.
In loco parentis
There are several reasons why violations of student rights are upheld by the courts. One of the most basic reasons is known as in loco parentis. This Latin phrase basically means that while a student is in the custody of a school, the school can and often should act as a parent. In this duty of the school, many decisions can be made that are outside the normal governmental purview.
http://www.usconstitution.net/consttop_stud.html
When a parent fails to be perfect, or a child fails to obey perfectly, it does not mean that government spontaneously gains additional powers.
Being a parent isn't easy but Government as a Parent is a nightmare.