If Czechoslovakia is like most other countries where people pay taxes for public education regardless of whether or not they have school-age children, then your suggestion makes no sense.
Is the state decides not to grant you the service, for whatever reason, then it should give you the money it would otherwise have spent in order to provide you with said service. Else you are subject to discriminatory treatment by the state, based on your personal decisions.
The parents don't approve giving their child a vaccine they consider experimental/risky/unnecessary, they do this in full use of their reason and with the children best interest at heart. The State decides no to provide educational service to the child, but the child still needs an educational service. The right course of action would be for the State to give the parents the amount money it would hav spent, so the parent can contract the services of a private educational institution that would give the child the education the child needs.
Sure, but some parents are unfit to take decisions for their children, and quite apparently the culture in the US seems to be religiously (pun intended) on the side of the parents.
In Europe, the fear of government in that regard is less expressed and the fear of parents mistreating their children by not giving the proper health-care or education overweighs that one in general.
If there is a criticism on that point, I hope it will not diverge into hypotheticals but rather concrete current examples, where you think that is misguided.