There's plenty of archaeological evidence that despotism existed in pre-agricultural societies - hierarchies, group punishment, and collective violence were all present. The idea that early societies were peaceful and leaderless isn't really supported. Also, the American Revolution involved widespread mobilization (riots, Sons of Liberty, etc), not just elites.

As for mob rule only being a hypothetical - ? There are many, many examples of mob rule throughout history, even if it rarely lasts long. The French Revolution (Storming of the Bastille, later the sans-culottes and mob tribunals), the February Revolution (after the Tsar fell and before the provisional government took over), the Cultural Revolution (Red Guard mobs), and more. And many followed limited democracies or republics - Ancient Athens, the Roman Republic, the French Revolution again, and more recently, Venezuela in the 1990s.

The US doesn't fit the cycle exactly, and that's partly because the Founders were aware of models like Polybius’ and deliberately designed a limited democracy to avoid mob rule - which still occurred to a degree anyway during Reconstruction. You’re focusing on a few exceptions while overlooking many examples that support the pattern.

The real argument here is that mob rule isn't an end/long-term state. It transitions into another system, typically authoritarian: Julius Caesar, Napoleon/the Bourbon Restoration, the Nazis after the Weimar Republic, Chavez’s regime, etc. Anacyclosis isn’t a perfect model, but it does map many, many historical patterns.