And here's an interesting thought. Even when some ancient city-states had clear hierarchies favoring rule by an elite man or small group of men, the ruling hierarchy would often work very hard to maintain the illusion of something more egalitarian.
For just one example, think of the Roman Republic, and even the early empire. Until about the second or third century CE, Rome was an oligarchy run (often rather ruthlessly) by a small circle of ultra-wealthy families.
Yet those families were devoted to more democratic rituals, with constant direct elections by the people gathered in either their tribes or their classes, magistrates supposedly answerable to the people through their elected tribunes, etc.
But these forms that they were devoted to were mere illusions. The frequent armed conflicts that brought down the Republic were fought between factions of oligarchs. The conflicts rarely had anything to do with actually preserving or bringing back egalitarian practices, even though both (or all) sides would usually claim to be doing that.
Julius Caesar was beloved by the common people because they perceived him as a force for stability and for protection of the common person. (And because he was very generous with his money.)
But his standing up for the common people was as much an illusion as anything. He claimed not to want to be a king, and he claimed to stand for democratic government, but he always fought wars in the interest of his own enrichment and the enhancement of his own personal power. The idea of Caesar as liberator was always intentional propaganda on his part. And he was damn good at it. (I'm not saying that people were wrong to yearn for stability and to welcome whatever stability he and his nephew Octavia /Augustus eventually achieved. Just pointing out that the egalitarianism he claimed to stand for was not his sincere position.)
Anyway, something of a sidetrack, but I think it's interesting that some ancient cultures revered egalitarianism even when they weren't actually practicing it. I surmise they might have revered it because they remembered it in some culturally important way.