Tribal organization is different than hierarchy. Hierarchy is actually fairly recent; forms of it existed in terms of social class structure and rule for a few thousand years, but today's hierarchy was invented by the modern Christian church.
Humans are social animals, so we absolutely need some form of social structure to function. But how that structure must work isn't rigidly defined. What is clear, though, is that since we aren't innately rational creatures, we do need a simplistic form of governance (typically a power structure of leaders).
By saying "power structure of leaders" you're conflating leadership with power (and governance does not make us any more rational). For example, tribal "war chiefs" in indigenous groups were often seen as analogous to monarchs because that was our Western frame of reference at the time, but in practice their leadership was entirely consensual: if they were no longer needed, they abandoned their role and if their leadership was not considered satisfactory (i.e. poor performance, erosion of trust or abusive behavior) they were readily replaced.
Human groups are first and foremost consent seeking. In order to override consent, you need violence. Any governance that is not consent-based (not consensus-based, those are different things) requires a threat of violence to persist itself. Whether it's the direct threat of the king's men burning down your cottage and killing your family or the state sending armed law enforcement officers to take away your things and incarcerate you or the indirect threat of your employer firing you and taking away your source of income that enables you to have a roof over your head and food on your table.
It's worth remembering that most still widespread beliefs about animal hierarchies are likewise tainted by the power structures in which they were first described. I think the most infamous example is the myth of "alpha wolves" that even its author now regrets ever having published because it was based on a bad interpretation of the behavior of wolves in captivity (i.e. a man-made artificial environment), not the natural group dynamics of wild wolves.
There is no general statement to be made here -- some tribal organisations are hierarchical other's aren't (including the ancestors from my fathers side as recent as 100 years ago). For decades now western ethnographers and cultural anthropologists seem to have projected their dissatisfactions of their own world onto their subjects -- which is something more insidious than the frank judgements you get to read in first-hand encounters during the early modern period. This has reached a certain pitch in current years by the overt activism of modern X-studies.
> today's hierarchy was invented by the modern Christian church.
On the contrary, the Church was responsible for destroying the hierarchical structure of my father's people via colonialism. Just to repeat: I am trying to point at a strange phenomenon that one notices in modern western academia: it is precisely the unaddressed universalising, really, Christian beliefs of, say, a current professor of cultural studies coupled with a dissatisfaction with her own culture that leads her to attribute what is considered good under her ideological commitments onto the natives and the other way round. For example, the idea that all men are equal would be flat out 'devilish' to my father's people even 100 years ago.
Humans are social animals, so we absolutely need some form of social structure to function. But how that structure must work isn't rigidly defined. What is clear, though, is that since we aren't innately rational creatures, we do need a simplistic form of governance (typically a power structure of leaders).