A simpler alternative assumption could be this:

1. sophistication is driven by specialization

2. the ability to specialize is driven by access to surplus energy

3. before the advent of agriculture bands of humans simply did not have the excess calories available to them to support a priesthood and philosophers and bureaucrats, etc.

Or maybe they simply choose to not spend those excess calories on philosophers and bureaucrats because doing so provided no immediate benefit? We have evidence showing that the rise of civilization and agriculture were a net negative for an average individual. It seems that at least in Egypt and Mesopotamia climate change, specifically an end of warmer and wetter climatic cycle, is what pushed people into fertile river valley. Most people would had probably preferred to remain hunter gatherers had that been possible or even independent farmers (which is what happened in the rest of the world.

The people in Mesopotamia (and in other similar areas which were slowly turning into a desert) didn't really have a choice. Building and maintaining irrigation systems takes a lot of people and coordination. Since most would probably prefer to be the ones handling 'coordination' aspect rather than digging trenches in the mud priests and philosopher classes had to appear to maintain social cohesion. It's much easier to convince peasants to give X% their harvest to the local strongman when they know that he's an divinely appointed king or maybe even a living god himself.

That is definitively not a simpler assumption. Each of those bullet points is itself a new assumption.

> sophistication is driven by specialization

Sophisticated technology is driven that way for sure, Sophisticated culture, I would argue, does not have those preconditions.