I won't name names, but a company that I worked for was very web-like, which felt good at first because it seems more "fair" or democratic, but it lead to constant confusion, infighting, communication failures, etc., and I discovered that it lead to two forms of employees: hogs that managed to eat more from the trough through clever maneuvering, and "homer simpsons" who figured out they could be lazy and not suffer serious consequences since their title was nebulous and the chain of command was diffuse(an individual with poor performance didn't reflect that badly on a superior).
The team that I worked on functioned mostly as a web, and that actually worked well because we were only 6 people at most, but an entire company functioning as a web is a nightmare.
Congress and President have, as I understand it, a mutual veto - but in the case where both are controlled by the same party, they tend to defer to the party organisation, which in turn defers to the President. Where they don't, you get shutdowns.
The President is generally immune to congress until they do something that gets enough congressional support for impeachment. This has proven extremely hard to do so far. The President also gets significant say over any issue that doesn't strongly unify congress.
Thus, for an issue that is popular in congress and unpopular with the President, but not popular enough in congress to override a veto, the hierarchy does President > Congress (a > b means a is above b). SCOTUS almost never gets involved when it comes to passing laws.
When it comes to an issue that is popular enough congress is willing to override a veto and which is popular enough with voters that congress going against the President on it isn't a threat, then congress > President.
I don't think anyone is claiming there is a simple hierarchy that consistently applies regardless of scenario. Even in a classical monarchy the hierarchy can shift for extreme enough scenarios.
There are likely shadow organizations in the Congress and White House with their own (unpublished) hierarchy, but probably not in the SCOTUS due to its size and the implicit potency inherent in being a Justice.
When your group grows beyond 9 people, that gets harder.
That's the 3 branches of government with its checks and balances.
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?
