it's a trope of history going back at least as far as Ibn Khaldun that amazingly often the barbarians roll over civilization, and conquer everything, only to fall victim to the next barbarians themselves.

That does happen a lot, but the barbarians in question tend to be nomadic pastoralists, very rarely foragers. About the only exceptions I can think of happened in immediately post-contact North America, and that was a fantastically turbulent time culturally -- between the introduction of horses and 90+% of the initial population getting wiped out by disease, pretty much everything would likely have been up for grabs.

I don't know offhand how healthy or long-lived pastoralist cultures tended to be by comparison with sedentary agriculturalists. I do know that they generally fell somewhere between foragers and agriculturalists in terms of sustainable population density.