I think this is a very important topic so thanks for opening this discussion!
Words are just words and everyone understands them a bit differently, but I'd say hierarchy yes, authority no. People still often think kids need to be formed and shaped into good human beings, which is a highly dangerous and possibly harmful task to undertake. Kids are wonderful loving wise beings as long as they aren't screwed up. Yes they need to be ..let's say provoked in certain ways so they go out and explore, so they become sociable. They need boundaries so they feel secured by their parents and become socially tolerable. A good way of telling if that's going well for you is when other kids love to play with your child.
A child can develop healthily when the parent truly listens to the child, actually understands the child's struggle, but doesn't try to force it's development into a certain direction and doesn't overprotect or spoil them unnecessarily.
The great child-psychologist Alice Miller told the story of once meeting a very loving wise old man in the park, who was wonderfully attentive towards children, truly listening to them on one eye-level, he was emitting an atmosphere of harmony and peace. About his mother he said while looking up: "She loved life". And I think that's it right there. Most people would say "She loved me". He said "My mother used to sometimes wake me up very early, so they could watch the sunrise and the wonderful misty morning atmosphere whilst cuddling together." He said that he loved her so much in these moments. And he was still carrying this love with him as an old man, and he shares it with others. If people decide to act through fear though, and let's say demand respect from their child, the result will be conflict.