Why society's focus on violence?
Humans have been competing for resources since the dawn of humanity - either against other apex predators or against other tribes or civilizations. Civilizations invented their own heroes of Legend and today's Superheroes are just an extension of that. It glorifies the ideal Warrior. It gives a civilization something to be proud of and aspire to: the ideal protector. As mentioned previously, play hones ability and survival instincts. Strategy games hone strategic thinking and D&D was born out of a strategy military game.
It's fun to pretend to kill dangerous things from the safety of your own home and live out the 'violent survivor' story when you have nothing to worry about. I doubt that, in any country where there are mass genocides and atrocities, or civil war that people are sitting in their house role-playing. They're living the violence and trying to survive. (but maybe I'm wrong - I'm just making an assumption).
So, we in our first world countries, (-mostly, on the whole - to avoid a broad sweeping generalization)are far removed from actual violence. Playing it out and murderhoboing is exciting and fun when the reality of violence is, in actuality, pretty terrifying.
It would be easy for D&D to put in a 'Take Out' mechanic that lets the victor of a combat narrate how an enemy is defeated. The final blow of the sword cuts the person's belt and their pants fall down. They've been utterly humiliated in front of their peers and surrender. Honestly, it would be easy to do and much more interesting than flat out killing everything. Also, DMs have enemies fight to the death. Weird.
It would be interesting to give enemies a threshold of hit points. Once you go over the threshold, the enemy will surrender. Clever, careful or fearful enemies have bigger hit point pool over the threshold, giving them more opportunity to surrender in a combat. While things, like undead, have a threshold total of 0. Meanwhile, those hit points over the threshold are used as a bonus for things like social conflicts and negotiations. I mean, there are options for social conflicts in many games. D&D could easily incorporate them or create their own - even if it was as an 'add-on' rule in the DMG.