Nah, we are biologically built to function in bands of no more than 300 people. Hierarchies are just the basic level of abstraction allowing bands to collectively form tribes, nations, and empires.
It's nowhere as clear-cut as you try to portray it. First of all, there are differences among primates, how are these hierarchies structured and some of it is also, surprisingly, cultural. (Look for example at work of Robert Sapolsky.)
I for example believe that hierarchies are a cultural artifact of civilization, not a biologically inherent human value. The inherent human value is deference to authority, which is useful to maintain existing order and generational memory (and is the basis for what we typically call "conservative"). In tribes of 300 people or so, the hierarchies are easily challenged. In a civilization of 1000s of people, with incomplete information, this is much more difficult.
(That being said, I think there are individuals who do not share typical human values, and try to subvert those for their personal benefit. So these individuals might subvert the value of deference to authority to create a hierarchy from which then they personally benefit. Just like existence of somebody, who might always take and never give back, doesn't invalidate reciprocity as a typical human value.)
And in fact we increasingly live in a world where everybody is a member of multiple independent social hierarchies, and these apply situationally (and it's not even clear they are always needed). This really strains the claim that humans inherently favor hierarchies (which there should be only one), rather than just simply defer to authorities (which might be multiple or even chosen by each individual independently).
I don't think deference to authority is inherently human, there are plenty of humans who resist authority to various degrees independent of socialization. It might be a "median" human quality though
There is a difference in belief that the authority is good in general and accepting the existing authority; when I talk about deference to authority, I mean the former, but it doesn't always translate to or imply the latter.
I think it is a useful value (and so it evolved in humans), because it forms the basis of parent-child relationship and the transfer of culture. So as young, we reluctantly defer to authority of our parents and other elders, and as we grow older, we begin to believe in the existence of authority as necessary to prevent the cultural collapses due to social experimentation gone wrong (which might result as pursuit of other human values). The fear of such cultural collapse (and the need to prevent them, through authority) is the focal point of conservative values.
Of course, in modern society, this gets pretty muddled, because the rate of change in societies has accelerated and actual authorities (in power) are often younger and change too quickly to really facilitate the transfer of life experience between generations. From this grows various forms of resentment, which is further shaped by ideological propaganda. My point is, I believe that the demand for more authoritarianism comes from people who believe that culture (they grew in) is in peril and want to slow or stop the rate of its change.
It might also be a reason why people believe in God - as Dan Dennett pointed out, it's more like that people believe that belief in God is itself a good thing, rather than necessarily believing in God as an existing being. This is, again, a manifestation of the belief that some authority is required.
Wolf packs work like a family because they are families. For some reason people used to believe that packs were groups of wolves from different families, but that is not the case. Maybe because feral dogs will form large packs that are not from the same families and they assumed wolves did the same thing.
Biology or no, there are problems with living in giant hives as we do now. We simply don't know (personally) the people who rule us, so there's no question of rule by consent. We don't even know people who know them.
Dunbar's Number squared seems like the ideal population size. Enough people that some level of privacy/anonymity is possible but not so many that rule by a sociopathic elite can emerge.
Proof of it being biological? Look at other primates. They form groups of way less than few hundreds and still maintain (strict) hierarchy.