All communist governments (not all communist movements, and this is actually the source of many breaches between communist movements that aren't governments, particularly in the West, and communist governments and the movements aligned with them) are rooted in Leninist vanguardism, a specific and particularly authoritarian rewriting of Marxist theory to avoid the dependence on developed democratic capitalist society with broad proletarian class consciousness and grassroots leadership as prerequisite to communism.
But the French Revolution, which was ideologically far from authoritarian, had a lot of the same practical problems; trying to run a state with active counterrevolutionary forces tends to make people authoritarians for what they see as temporary and pragmatic necessity as a means to achieving a more free end-state (and defenders of Leninist vanguardism would probably see it as just that!)
Americans sometimes forget that what we call our “revolution” was not an anti-elite revolution but an elite-led regional separatist movement coordinated by the local governments acting in concert, and so avoided many of the challenges found in genuine revolutions.
That said, it's still a far cry from the scale and severity of violence seen in various later revolutions.
One nit: The American Revolution was led by elites, if by "elite" you mean "wealthy and influential". But it was not led by elites, if by "elite" you mean "nobility". In that sense, it was quite anti-elite.
To me that would qualify as elite. Not sure how much local nobility there was in the area, but certainly the folks leading were the local elites IMO.
It was led by the landed elites, which didn't happen to generally have titles of nobility in the colonies, because the evolution from a feudal to a capitalist property structure had progressed pretty far before the US was colonized.
OTOH, the difference between a slave estate and an English feudal estate is mainly that the master of the former has even greater power over and less obligation to the subjects, so the difference between the elites you are distinguishing may be even less substantive than it seems at first glance.
But the political theory question might be: Why have seemingly all communist movements and governments been authoritarian?