I would have guessed that a lot of that "meshing together" involved one side surrendering sovereignty or identity to the other (whether by force or pragmatism). But, as you say, the wars get more coverage. Do they also happen all the freaking time too? At least enough to not make it certain and obvious that they'd work together?
Take a look across allllll of history. And count the years and months where there were wars across the world. And count the years and months where there was no war, or at least none written about. None remembered.
And then consider that even in the places where there -was- war, the rest of the world -wasn't- fighting.
War and Violence are punctuation at the end of countless long sentences that we ascribe great importance to. There's a reason the history books don't talk about "Peace breaking out".
In Ur, in Mesopotamia? People controlled a valuable resource and others sought to join them. No "Surrendering of Sovereignty" or identity through force or pragmatism. They just moved into Ur with their culture and their lives and... that's it. Over the course of generations their children's culture became a mesh of the two. And their children even further, and on and on until Ur's culture became a blending of the different "Tribes" who joined together within it.
Because immigration and emigration were things even before they were legal terms. An Akkadian could travel to another city, sell his wares, buy a place to stay, and become a part of the new city, and that was just... y'know... how it works. No loss of identity or sovereignty. He just moved. Same as today with endless people crossing borders so long as the people within the borders aren't massive jerks about it.
Most of our understanding of early history and prehistoric "Tribalism" is based on modern interpretation of violent events as the norm. They were never the norm. They were and have always been the exception. The special things we make note of when it happens and demarcate peace by bookending it with wars.
All you have to do is check the dates and locations in your history books. Most of history was, and will be, people living quiet, normal, peaceful lives. Stressing out about deadlines and relationships and politics and crops and newfangled technology... and their kids being "Uppity".
Mesanepada may have killed Lugal-kitan to make Unug/Uruk into Ur... but then he ruled for 80 years. And his son for 36. And his son for 40. And his son and his son and his son. And in each of those following monarchies there was a ton of peace, a little war, and a lot of people just being people.