Interesting. If you look at history, it is precisely governments and empires that produced more violence than anyone else. The bloodiest, most devastating wars are all the result of government action. Even the most bloodiest anarchist in the world cannot come close to what an average "peaceful" state has done in his lifetime.
Violence is inherent, at least at this point of our development, in human species. Question is, what brings about more violence. I would argue, that it's the idea that we need some sort of government. This very idea creates the incentive for sociopaths and bandits to get into politics and allows the ruling class to continuously keep fucking the population.
> I would argue, that it's the idea that we need some sort of government.
It's not an idea at all. It's what OP referred to as a 'power vacuum'.
An anarchy sits at the top of a local maxima, where a little nudge in any direction is enough to set the whole political situation careening toward violence and the acquisition of power all over again.
An anarchy can only survive until the first person gets enough allies to put their boots on the throats of the rest.
So while it's true that an anarchy is such that you can effectively only cause people nearby you to be killed, it is an inherently unstable political situation. Witness the stateless tribal areas of Pakistan; despite the lack of the state there is assuredly a boss. The power vacuum has been filled by local tribal warlords.
An anarchy surrounded by Western democracies might even be safe (that is, from external conflict), but a world full of anarchies will not remain a set of anarchies for that long.
Violence is inherent, at least at this point of our development, in human species. Question is, what brings about more violence. I would argue, that it's the idea that we need some sort of government. This very idea creates the incentive for sociopaths and bandits to get into politics and allows the ruling class to continuously keep fucking the population.