I think it is a more practical relationship than something intrinsic. Power (or relative power, really) comes from consolidation and control of resources or agency. Hierarchy is a very efficient and scalable topology for command and control, helpful to manage such a consolidation.
But, other methods might be possible to wield power without hierarchy. An individual with massive wealth can consolidate financial power. They certainly depend on a system that enforces rules and protects financial interests, but can you really call that hierarchy? They might perform significant, world-changing transactions but they do not continue to control the assets once they are traded. It might be a hierarchical distribution in the "trickle-down" sense, but is not hierarchical control nor planning.
Or, if someone obtains some sort of scifi doomsday weapon and uses it to extort others, is that expressing hierarchy?
But, other methods might be possible to wield power without hierarchy. An individual with massive wealth can consolidate financial power. They certainly depend on a system that enforces rules and protects financial interests, but can you really call that hierarchy? They might perform significant, world-changing transactions but they do not continue to control the assets once they are traded. It might be a hierarchical distribution in the "trickle-down" sense, but is not hierarchical control nor planning.
Or, if someone obtains some sort of scifi doomsday weapon and uses it to extort others, is that expressing hierarchy?