Isn't human history merely a long series of wars punctuated by very short periods of peace?

It is. Unless, of course, it isn't.

There's always a war going on somewhere. 

Depends if you count only the written records; they begin with the Egyptians and Hittites, which is quite late in human social evolution.

Also depends on what phase of history, the conditions and the place.

Paleontologists have found no evidence of war until tribal populations grew large enough to suffer from lack of resources and begin encroach on each other's territories.
In the 60,000 years of Aboriginal occupation of Australia, there is zero evidence of warfare. There is evidence of severe punishments for individual transgressions of law. War here didn't begin until the white colonials arrived with guns. This post was edited by inky at June 13, 2020 2:12 PM MDT

sounds like it