I read that book back in 2011 and I don't think it's aging well. While I greatly respect Pinker as a political thinker and theorist, I found his ideas about ancient societies unconvincing.
It's really, really hard in archeology to be certain of almost anything. I question the robustness of a lot of Pinker's numbers.
Putting that aside, if we look at just the last 2,000 years, what stands out to me is how closely periods of intense violence correspond with periods of intense Climate Change. Pinker sees a gradual decline in levels of violence, I see episodes of peace marked by good weather (think Medieval Long Summer) punctuated by periods of intensive violence.
I mean really, the population of the Mediterranean basin and Europe circa 150AD was around 75 million. By 650AD it had declined 50%. This was due to a cooling climate, not because of flawed social structures.
We have had a period of great stability and peace, the lesson of history is that it isn't going to last.