Although people governing themselves is the whole idea.
What you just described is "anarchism". All those synonyms you cherry-picked from your dictionary are instances of the same word being used to mean different things – notably by
opponents (rather than proponents) of anarchism. What you just did is akin to getting a definition of "conservative" from a modern leftist. The
whole point of those usages is to describe a discreditable (but fantastical) philosophy that nobody would adopt. And yet somehow you imagine that to be identical with anarchist theory as espoused by, you know, actual anarchists? I promise you that a dictionary is not capable of thinking for you.
It's certainly not the "idea" behind the US, rhetoric to the contrary notwithstanding. A strong centralized government is basically the antithesis of self-rule; it's basically the definition of "oligarchy".
The ancient Saxon common law was largely anarchistic, as was the ancient Irish system. Law without rulers works just fine. Actually, given that law
with rulers has without exception devolved into corruption every time it's been attempted, I'd say it is, in fact, the various -
archys which have never worked throughout all of history.