I don't think tribal humans actually killed each other that much. They probably fought much as how the medieval peoples fought. You would posture and intimidate your enemy by shouting and throwing missiles, and when your enemy fled that would be it. If they surrendered and you wanted to dispose of the adult males you would find ritualistic ways of killing them that remove the responsibility of the crime from any one person or distance you from the result (see: lynch mobs that hang people together, firing squads, burning witches at the stake, having someone whose job is to be an executioner). If people have been brainwashed through religious or cultural beliefs they can convince themselves that they were not responsible for a crime as a mental defense mechanism (see: the Jewish Holocaust where people were dispassionately throwing corpses around, various examples of deranged people who believe God was controlling them when they killed).
And yet peasants were able to poke big sticks at other peasants no problem? I wonder if culture has changed.
Your mistake, I think, is in assuming no one in medieval times had any problems with killing each other in combat just because there are no recorded instances of people becoming depressed after killing someone in combat. What we do know is that there is no culture in existence that hasn't punished people for murder, and also had a form of murder that was considered justified. That in itself is evidence for the instinctive urge to not kill one another to be ingrained in us as a species.
But, to take another page from David Grossman, I do think that people back then who slaughtered their own food had more knowledge and respect for the act of killing itself, since it was a time when families slaughtered their own food.