I agree with all of that. We do have an instinct for cooperation, although this evolved in a tribal rather than a humanistic context, which made for inevitable conflict between tribes. And yes, the alphas aren't always just physical dominators since they often excel at marshalling social support.

Still, however intuitive morality might be for social primates, this morality operates in societies that routinely empower those with psychopathic tendencies. So morality is at least partly a reaction against this darker trend. It's something like slave morality in Nietzsche's sense.