It's not necessarily a blanket rejection of authority, just a condemnation of the forms of authority that end up having a stratifying and totalizing effect- that is, when someone is considered to be an authority that all other authorities are subservient to, when some people are seen as categorically more valuable or more deserving than others, or when as an individual you are put and kept in a lower category regardless of your volition and efforts.

I can’t imagine a world where the wisest, most knowledgeable, or most capable people aren’t given some amount of acknowledged power

The great thing here is that wisdom, knowledge, and capability aren't one thing. There are lots of different ways to be wise, lots of different fields to be knowledgeable in, lots of different skills to be capable at. Instead of thinking about a comrade, "Frubbins is the wisest", we should be thinking "Frubbins has outstanding wisdom and eloquence in motivating and inspiring people".

We can take things like the theory of multiple intelligences from psychology, and separate political domains from First Nations cultures, and a lot of other stuff, and start to get an understanding of how people can develop themselves for various proficiencies, without having to "rank" the skills or the people. There will still be a hierarchy within each skill or domain, but it won't extend beyond that field. Between the two of us, I might be the better teacher and you might be the better event planner and meeting facilitator; these don't need to be stacked up against each other.