Primates (and most other mammals) usually recognize, respond, and require a male alpha. There are female alphas in some species, but even they usually submit to a male. Politically incorrect or not, this is also true for H. sapiens. We are able to see this as a tendency in history, marriages, business, and governments.
As with all things evolved, natural selection is responsible. The fact that alpha males exist is evidence they were required for our species to survive. Male size and androgens (especially testosterone) were critically beneficial to our species -- as were estrogen-rich, fertile females. We are here because our fathers were the strongest males and our mothers were the most fecund females.
Is this same phenotype required today? Probably in the few primitive hunter-gatherer groups that still exist. Probably not in the "civilized world" most of us live in. If we change our breeding habits, if females begin mating more with Omegas and less with Alphas, our genome will change. Our phenotype is the result of both our environment and our genome. Our environment has certainly changed in the last few centuries and if our civilization holds together, I expect our genome to follow suit. But, it will only change as the result of natural selection, and natural selection will be determined by breeding. As more females breed with intelligent and less aggressive males, our species will become more bonobo and less chimpanzee -- and the jocks will no longer get the most chicks.
Until that time, our species is uniquely able to short-circuit our genomic instincts (to a degree) -- and we see it happening. More females are stepping into roles that are classically male-dominated (business government, breadwinner, etc.) , and males are (sometimes reluctantly) accepting it. More females are also breeding with less agressive males.
Is this a good thing? In biology, "good" is what helps ensure the survival of the species. "Bad" is what leads to extinction. Natural selection is neutral -- it doesn't care. It's simply the result of breeding. There have been species that have been "naturally selected" into extinction when reproduction failed to pass on an adequate genotype to cope with the environment.
Now, I'll take off my zoology hat and put on my grandson's ball-team hat -- to give some personal opinions. Last century, our species developed the capability to destroy itself. This ability being in the hands of primates (male and female) who still instinctively respond positively to the aggresive, alpha male is somewhat disturbing. For those skeptics out there, I point to the (elected or otherwise) leaders of America, Great Britain, and almost all other nations.
If our species survives, it may be because female (or far less agressive male) leadership occurs in time. So, all you fertile ladies out there, for the sake of your species, do NOT breed with agressive males. Find a smart, gentle wimp and have a litter. Hopefully our species' need for an alpha male will then change by natural selection -- and our phenotype will more closely resemble Pan paniscus than Pan troglodytes.
BTW, on a side note. Phenotypical change is what Dawkins, promotes. However, he focuses on religious memes ("mind viruses") as what needs to be bred out of existence for the sake of humanity. Even if that were true (which it's not), that's attacking a symptom instead of a cause. Gentle religion, gentle politics, gentle marriages, and gentle people are what our species needs -- and that will only occur when gentle genotypes breed with gentle genotypes, religious or not.
(Of course, if civilization ever fails and we fall back to hunting/gathering ...)