Hierarchy presupposes a kind of cooperation that isn't the "natural state". The natural state is "might makes right, but don't push it, because you'll die of a bacterial infection".

Once one has a significant capacity for social behavior, all sorts of strategies open up, hierarchy being only one.

Chimps are usually comparatively violent (though displays of aggression are even more common than actual violence, and alpha males need to shake hands and hug babies too--support-building is even more important than strength) with a male-led hierarchy; Bonobos are more peaceful, with parallel female and male hierarchies and the female hierarchy seeming usually more important. Many baboons have a stable female hierarchy with comparatively transient males (who, transiently, may be at the top of the hierarchy, but it's really the female hierarchy that forms the core of the tribe). Hyenas simply have females at the top of a violence-enforced hierarchy. Elephants have females at the top of what seems to be respect-based organization, especially among Asian elephants where it's hard to discern whether there's really much of a hierarchy at all. Termites and ants have extreme control but a very flat hierarchy: queen on top, everyone else subordinate and usually equal.

And as you should very well know, penguins generally do not have a dominance hierarchy, rather congregating for mutual benefit but without enforced leadership.

So, no, although dominance hierarchies are common among social animals (because it's a simple way to solve conflicts in a less destructive way than might-makes-right), I'm not comfortable saying that nature "fundamentally works this way". The reason is that the fundamental is might makes right, but if you and your friends harmoniously cooperate, together you have more might than your competitors. So minimizing within-group conflicts is a plus, and while dominance is an easy way to do that, it isn't necessarily the best.