> the total extermination aspect in particular is a novel aspect of farming culture

Perhaps there wasn't a change in culture, but rather that farmer tribes were able to grow bigger? A hunter-gatherer tribe could be size-limited according to the available resources. Likely 2 neighbouring tribes would therefore be roughly the same size. Which would make it hard for a tribe to fully exterminate other tribes. Would you send all your fighters to take on another tribe, with the risk of none of them coming back, leaving you defenseless? What if a dangerous animal walks into camp while all fighters are away?

If a farming tribe could sustain double population, that would mean double the amount of fighters, thus it would reduce the risk greatly of sending out a large group of fighters.