Zarf,
"they [specializations] are only a byproduct of the creation of other social institutions you mentioned, and thus a reason why the other institutions thrived"
I'm glad you recognize that institutions caused specialization of labor and thus your more urbanized society and that this in turn further restructured institutions which thus further restructured specialized labor and urbanization.
But was this all a random chain reaction beginning with the first institutions, or was there some sort of guidance or control of the chain reaction? Sadly, the structure of the first institutions did in fact come to define the nature of our current society, more than most understand. Moreover, the structure of our current institutions did not come about solely as a result of advancing utilitarian benefit to society as a whole. In most examples of the restructuring of institutions, it occurred by design, according to the self-interest of those in control of the power to restructure said institutions.
First, to assume there was no design in the restructuring of institutions would be to assume there was no control over those institutions being restructured. And yet the very structure of institutions themselves requires there to be a centralized government in control of institutions in order for them to function or, for that matter, to be restructured. How, as an example, could there be a military without a chain of command, and, for that matter, how could that military modernize without a chain of command to issue its modernization?
Now, this brings us to the question of how often leaders of institutions have restructured institutions according to their perceived notion of the greater good to society at large and how often they have restructured said institutions for the betterment of their own (or decedents') self-interests. Weren't the Pharaohs more concerned with the grandeur of their Pyramids than the well-being of the slaves they drove to construct them? Likewise, did the ancient Grecian philosophers grant their women and their slaves the same voting privileges (and thus power to restructure institutions of ancient Grecian society) as they themselves employed? Were feudal peasants really as empowered to affect change to their societal institutions as the feudal lords who controlled them? Of course not.
Moreover, there are ample historical examples of when the restructuring of institutions of a given society occurred, it was done so in large part to pursue perceived benefits to those in control and not in pursuit of a utilitarian 'greater good' of society as a whole: ancient Egypt, ancient Greece, ancient Rome, Christian-dome, ancient Chinese dynasties, French Revolution, Russian Revolution, American Revolution, etc.. In all examples I can think of, it was the ones who were in control of the most influential institution of all, the military, which restructured that society's institutions according to their own (the victors') self-interest.
...
Have to go and do something else.
Anyway, I doubt there was much evolution of society. I see it as simply having been designed by the victors, for better or worse, not necessarily better, and, actually, ultimately, probably for the worse overall.
edited for clarity and typos