To further muddy the alpha male issue, note that the social structure of primates varies tremendously. Here's a list of several different species and a quick rundown of their social structure. Note that species in each type of social structure still exhibit differences of varying degrees. Baboons, howler monkeys, and gorillas all live in a one-male, several-female structure but each species has its differences.
Orangutans, (some lemurs and galagos live in a similar, but slightly different structure): females live solely with their offspring, while males live solitary lives, only coming together for mating purposes and the occasional random encounters. The alpha concept cannot apply here.
Gibbons, siamangs, titi monkeys, indris, tarsiers (and humans for the most part): monogamous family groups. Alpha concept does not apply since there is only a single adult pair and their offspring and the adults are monogamous. One extremely important thing to note is that wolves, the species where the alpha concept was first theorized, were later shown
not to have alpha males and females. Wolves live in monogamous family groups, with the mated male and female living with their offspring of the last several years.
Hamadryas baboons, geladas, langurs, howler monkeys, gorillas (and some human societies): one male and several females form a distinct family group. The male is often labeled as the 'alpha', but note that in many of these societies the females often band together and chase out other females, exert influence over other members of their group, and even
choose their own mate from several suitors roaming around. Notably the chosen male is often the one that displays
fewer traits we commonly consider to be alpha-traits. Males that are more cooperative and less abusive are more likely to be chosen. Not only that, but in some species the male can be chased off by the females (makes you question whether you're still an alpha male if your
women chased you off

). Alpha concept applies only questionably in my opinion since the males do not live in a dominance hierarchy.
Savanna baboons, macaques, as well as some colobus and New World monkey species: multimale-multifemale groups. No stable heterosexual bonds. Males and females have several mates. Social structure is dominated by a dominance hierarchy.
This is where the alpha concept applies best. The top male and female are the alphas of the group.
Chimpanzees: a 'fission-fusion' society. The size and composition of the social group changes over time and as circumstances change. Individuals may leave or join a community from time to time.Females often leave to join another community when in estrus, so males form the core of the social group. Note that this in itself has little to do with being an alpha or not. It just means that males are much less likely to leave their communities and so naturally form an unchanging 'core' for the community. Still, the alpha concept
sort of applies, as males form a dominance hierarchy.
As you can see, the species along our evolutionary lineage exhibit a wide range of social structures, and even our three closest species (chimps, gorillas, orangutans) are wildly different. If we accept that the current behavior of all of these species is an accurate representation of the behavior of our ancestors at various times, then the claim that the social structure of our ancestors can be accurately described by the alpha concept has to be balanced by the fact that many of our ancestors
did not have alphas.
It seems to me that our current social structure is based far more on cooperation and other traits that typically aren't considered 'alpha-like'.
Source for most of the above:
https://www2.palomar.edu/anthro/behavior/behave_2.htm