Lots of the deaths appear to be separate from war [1]. We have lots of evidence of violent crime in non-state socieities [2].
Where you might have a point is in the reduction of anonymous property crime. But that's just because small societies don't tend to have privacy. The property crime may still happen, it will just be resolved comunally or bilaterally using violence.
Having had the fortune to travel to many places, one thing I've learned is that crime stats tell you nothing by themselves. For instance there are many countries that have homicide rates comparable to, or even higher than the US, but where you could feel completely safe alone just about anywhere at any time, whereas in many parts of the US, or some other countries lower crime rates - that's certainly not the case.
So for instance a big one is interpersonal 'justifiable' crime, versus random crime. There are places where if you insult somebody's integrity, they will kill you. Add some alcohol into the mix and these sort of places can have some rather high homicide/assault/etc rates. But on the other hand in these very same places, your chances of falling victim to random crime is basically zero, so they feel extremely safe in spite of having many crime rates comparable to places that feel extremely unsafe.
And data about the nature of crime in the past is strongly suggestive that it also had a similar character. People would not hesitate to use violence in the case of interpersonal conflicts, but the chances of falling victim to random crime was likely significantly lower than it is today. And I think these are the sort of crimes that people mostly care about, and it being a result of social alienation does seem like a perfectly valid hypothesis, though I'm not sure if in present times South America and others would falsify it. From an outsider's perspective, they seem quite socially cohesive, yet have exceptionally high rates of criminality.
> your chances of falling victim to random crime is basically zero, so they feel extremely safe in spite of having many crime rates comparable to places that feel extremely unsafe
Where are you thinking of? What I've seen, more commonly, is societies with lots of crime having ways for the wealthy to insulate themselves for it and then, acting against a background that has normalised high crime, feeling very safe. Versus societies where everyone is more mixed together where folks are constantly paranoid about vanishingly-infrequent crimes.
One typical example would be Thailand. Its homicide rate is quite close to the US, yet the nature of crime in the country is very different. Your chances of running into any sort of random violent crime is basically zero. It also even challenges the economic integration argument since it's also atypical there as well - poor households being right next door to a luxury condo is quite common.
Lots of the deaths appear to be separate from war [1]. We have lots of evidence of violent crime in non-state socieities [2].
Where you might have a point is in the reduction of anonymous property crime. But that's just because small societies don't tend to have privacy. The property crime may still happen, it will just be resolved comunally or bilaterally using violence.
[1] https://historyandarchaeologyonline.com/bog-people-criminals...
[2] https://www.researchgate.net/publication/279610323_Violence_...