"There's no interpretative reasoning required when you're looking at a graph of the level of violence in society"
Yes, there is.
Imagine a society without justice/police in which people must fend for themselves. It would quickly deteriorate to the point wherein there would be a fair bit of violence.
Imagine you - the same person you are now - in that situation.
It would be a completely different dynamic of 'violence' and represent a completely different situation - and yet it could very well have little or nothing to do with our moral position (i.e. 'better angels').
Second - I think that 'war' is a completely different kind of violence than regular violent crime.
One could argue that the only thing that has made modern countries less apt for war is MAD, i.e. the fact that there's no real possibility for gain or winning outcomes, with nuclear weapons, the borders are largely frozen. Point being: a weapon, of all things, could have such geostrategic importance that it quashes violence, irrespective of anything else ('better angels') etc..
"There is a wealth of evidence about how bad things have been over the past 200 years or so, and every metric shows that things are getting better. "
This is also false.
From 1960 to 1992 crime in the Western world grew by 800%.
That's almost a 50 year period out of 200 and is not 'cherry picking'.
Violent crime today is still about 600% greater than it was in 1950.
It's a paradox few want to face: that the 'liberation' of the 1960's was also coincident with a massive increase in crime, which peaked in 1992 and has come down somewhat, but still quite high compared to the 1950's.
Anyhow - I don't think it makes any sense to look at violence outside the big contextual things.