The parent knows instinctively that if they're working and setting an example for their child that means that child is more likely to be in school more likely to stay out of trouble and more likely to complete their education.
The problem of how we finance the welfare state should not obscure a separate issue: if each person thinks he has an inalienable right to welfare no matter what happens to the world that's not equity it's just creating a society where you can't ask anything of people.