rather than of cooperative living between some Neanderthals and Sapiens?
Of the great apes, I think that it is the chimps who are the most spontaneously aggressive. Chimps have also shown in studies that they lack the willingness to delay gratification for a greater reward. Gorillas can be aggressive against other gorilla troops, or if threatened, but generally are calmer than usually believed. And, from my courses on apes and evolution, bonobos are less aggressive than humans and inclined to settle disputes with sex in order to create cohesion and harmony.
Yes, sapiens does pre plan aggression to gain territory, status, etc. But we also become spontaneously aggressive and murderous. Road rage, crimes of passion in the moment, spontaneous mob rage and attacks. (I was able to diffuse one of those once, thank God, by extending friendly overtures to their target, whom I happened to know from having once worked at the same company. She then became less of an "outsider" to the mob and was at least superficially perceived as 'ok')
I agree that sapiens has become more complexly organized in the process of civilization, which could be called self-domestication. But tribal societies also have some very sophisticated social structures, even though lacking the technologies of societies that we call civilized.
I think what you are referring to is the mental (and hormonal?) ability to delay actions and reactions in order to think of responses, to plan things in advance, and to plan and carry out some very sophisticated thought processes. That can be attributed to evolutionary brain developments as a result of evolutionary pressures beyond cooperation. Complex synaptic pathways, continued brain devolpment after birth, greater number of brain cells separate us from our ape cousins. It could be that cooperation in sapiens is a result of brain changes. Babies whose brains continue developing after birth are more dependent on adults for survival. Mothers caring for helpless infants are more dependent on others for protection and food.
The continued brain development is a result of becoming bipedal. Changes in hip placement and size as a result of bipedalism made it necessary for babies to be born before their brains were fully developed. So the changes you mention look like a result of physiological evolution which then caused a corresponding evolution of social behaviors.
Neanderthal was bipedal. Neanderthal brain cases were larger than ours. They had a well developed took kit and social behaviors - jewelry, ceremonial burials, caring for the disabled, art. They were not as different from sapiens as often believed.
Your premise seems to be that Neanderthal went extinct because they were less socially developed than sapiens. More likely, IMO, is that they went extinct as a separate subspecies because they WERE as social as sapiens and interbreeding diluted their genes until they were absorbed into sapiens, leaving only trace DNA.
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