There is overwhelming evidence that this is an intentional strategy in contemporary forager societies. I even gave an example in the OP. Why would it have been any different in the past? The incident that you recount speaks to this as well.

Yes, humans are much better at sharing food and taking care of their social group than other primates (and other hominin species) but many, many anthropologists agree that enforced egalitarianism is a central adaptation of human evolution - something that was noted and supported by several different subject matter experts in the OP.