I'm pretty sure that being elite is a symptom of running things, not the cause of running things.
By definition, a society’s elites always run things…
Pretty damn well in the long run!
Each of the French Revolution’s successive governments had their own sets of elites. (La Révolution itself had its elites.) Arguing against elites as a category is arguing against hierarchical sociology. It’s inchoate. We don’t have an example of a society without elites; we barely have examples of social animals without hierarchies. (Zebra herds.)
And speaking of the French Revolution, the elites ex post facto were not only mostly the same as before, they escaped with so much money and wealth that it’s actually debated if they increased their wealth share through the chaos [1].