The job of a parent is to teach his child how to be good adults. The job of a child is to become a good adult.
This fetishising of children, which started in the victorian era, has a strong connection to nihilism. Adults did not like responsibility. They did not like the fact that they were in charge. They craved "the good old times" when they had no worries and a loving parent told them what to do.
I think it's clear why a nany state sounded to them so appealing.
Not only do we need to teach children to be independent. We need to teach them to love and cherish their independence. And that is done by pushing them to take as much independence and responsibility as they can, and be proud of what they achieve with it.