I don’t believe there is an alpha human in every relationship, although there may be one person that decides to become the leader it is not an alpha type situation, however o would like to point out that although our social system doesn’t usually have an alpha, it has been shown throughout history that in the realms of Politics and economics there is always an alpha.
Chimpanzees, aside from being the closest living relatives to us in the animal kingdom, are extremely similar to us even in behavior.
(yeah not entirely, but if you read up on it they have a family structure, cleaning techniques, and they will mourn, not bury that I’ve heard of, but mourn the loss of a family member)
However, competition I would point out has no more complex form, whether it is with a complex lingual system or with teeth and claws the outcome is the same and the damage done is similar. We are superior to other a species of animals in our mental capacities but in instinct we are still animals, animals that are willing to steal, kill, and beat others to survive.
Now personally I believe a form of democratic socialism would be the best way to go in terms of getting rid of the super rich, however someone would have to devise a system to prevent corruption
(same as a capitalist society)