Do you think it is criminally negligent for a parent to bring up their child without any education whatsoever?
Do you think the state should intervene to protect criminally neglected children from their neglecting parents?
Most people I know, myself included, would say yes to both questions, and therefore the establishment of compulsory education is at least in part directly intended to benefit the children. Education is shown to be one of the very few reliable indicators around the globe of both individual and societal prosperity. How we educate is always up for debate.. should we educate is typically not.