> Essentially the elimination of all unnecessary hierarchy and domination.
Not necessarily. Please see my other top-level comment in this thread.
Anarchy has a lot of definitions and sub types. Anarchy as complete lack of structure is always used to attack and denigrate it by its opponents, but it's not an inherent characteristic of anarchism itself. Anarchy does not have to mean everybody decides and we put everything to a vote.
Anarchy means you can leave whenever you want. Nobody forces you. No one has the monopoly on violence.
Free software is anarchic. It might have strict rules, and a tyrannical maintainer than only merges what he wants, but it's still anarchic because you can fork it.
Most people tend to be in anarchic relationship with each other, because no one can force something upon the other. That's something only the government does.
In fact, making money and profit does not have to be anti-anarchic. It's certainly against anarcho-communism, but that's just a subbranch of a wider social theory.