Tough call. Most of their waking time kids aren't with their parents. They are in school either with other kids or their teachers.
So if they commit a crime in school should their teachers be liable?
I don't have a good answer just saying parents don't have total control.
If we all stillived in tribal family farms. Maybe a child's action would cause a war. But if a child steals candy in their way home from school it seems silly to arrest the parents imo.