I don't really see how that is an even moderately defensible claim. Most obviously, writing was not something that developed by "humanity" that then allowed for greater development. Writing was a tool developed by particular groups at very different times under very different circumstances. And so we can look at examples of places that did not have writing and see that, even so, there were some pretty massive cities--Inca Cusco being perhaps the most obvious example. That seems to call into considerable question the existence of some sort of natural limit to non literate cities.

My assumption is that Hariri is doing the thing that is very common among those writing "global histories", particularly non historians/archaeologists, and is universalizing the experience of the "Fertile Crescent", Mediterranean and Europe. This history and "growth of civilization" is remarkably well studied, despite major advances in recent decades no other region really is in the same ballpark in terms of the depth and density of scholarly attention. The reasons for this are many and outside the scope of this question, but the effect is that popularizing "global histories" have a tendency to be a bit blinkered in treating that particular story as normative even though a broader vision shows a truly bewildering multitude of possibilities large groups of humans can follow.

That said, even sticking to that narrative I'm not sure how he would justify that claim, given that the development of Uruk as a major urban site precedes the development of cuneiform as a writing system (not to mention all the substantial urban sites well before, eg Catalhoyuk). Admittedly there may be some context here I am missing.

A book that covers many of these issues and attempts to write a sort of "global history" in a much more rigorous and clearly focused way is Ian Morris's Why the What Rules; For Now.

I should also note that Sapiens was pretty poorly received by scholars. I haven't read it and can't comment outside of an instinctive distrust of the framework it advances and the sort of accolades it has received.