Not really as much as I feel we think. Having read more about Authoritarian mindsets, which includes the rank and file authoritarians, not just the leadership, they’re actually happy to be reinforcing the hierarchy regardless of their position in it. They’re happy to know their place and to ensure the ranks are kept in place. It brings comfort to many people to know that their position, regardless of how awful it is, is being maintained properly.
This means that they’re entirely okay with a dictator and/or an oligarchy as long as the people on the top are “supposed” to be there.