Going from "I'm not a historian" to "it might even be the norm historically" made me chuckle.

It wasn't the norm historically. Depends on what period of history you're talking about, but indeed not all groups attempted to expand, though it'd be equally true that most of these were because the group was not able to.

In terms of assimilation, it happened often that a cultural victory would still lead to military confrontation (before the fall of the Roman empire, many of their neighbours were, or considered themselves, romanised yet still either fought against Roman expansion or attempted to take territory from them for example). For as long as we have history, all the times I know of where a "group" assimilated into another group willingly, it was because the other group was militarily much more powerful and saw any peace as temporary: for example, Armenian kings giving away their kingdoms to Byzantium, to avoid uphill battles of resistance and to make sure their dynasty remained in power. And those times were very rare in history.

Of course, this might have been more common in pre-history (99% of our existence), but then again we have a lot of evidence to the contrary.