If you have no explicit hierarchy then an implicit hierarchy will start to form in most cases, which can be even worse. In many cases you have both.
Hierarchies are just an organizational pattern, a tool. There are neither a religion or "set in stone" as many think, they create communication choke points, induce unnecessary communication, cause "not our responsibility" mentality that may result in things falling through the cracks, have often the "Chinese whispers" problem to it, and so on. You cannot treat every problem like a nail just because your only tool is a hammer.
I think this is a pretty great statement of the converse of Conway's Law[1].
Because people want to exercise their influence, or protect their position, and form relationships and alliances.
I'd say "in evey case". And I'd say this happens whether or not there's an explicit hierarchy. Being articulate, or having knowledge or contacts, will get you more attention. The only way to mitigate this is through explicit processes, which have to be regularly reviewed. Meetings have to be chaired strictly. Everybody has to sign-up to the agreed processes.
These processes are time-consuming, and decisions can be slow. It becomes worse the bigger the organisation. I don't know how non-hierarchical decision-making can work in an enterprise where there are significant assets at stake; I've only ever seen it work in voluntary political associations in which non-hierarchical organisation is one of the prime objectives.
Hierarchies can be time-limited, or democratically limited, it just depends on the legal and organisational framework.
I'm not sure how far you can push a 3-layered organization, but it's absolutely something that exists on some scale, without a phantom organization appearing.