Certainly life improves via cooperation, and humans have thrived on it. But I think claiming our bare survival depends on it is a bit extreme.
Not extreme at all. This naked ape's strong suit is that it has the intellect to cooperate very effectively. Come on and look at us, we have no claws, no body armour, we can't run very fast, we have to make clothes to keep us warm, and our children are dependent on us for at least a decade. A single human may survive but not thrive. Our species survival was based on it's ability to cooperate in small groups. A punishment in many societies used to be banishment. If there was no other settlement or people you could join up with, this was almost as good as a death sentence. I think you serverely underestimate the need for people to cooperate for survival, especially in ancient times.