If all were internal monarchs, i.e. sovereigns of themselves acting harmoniously and morally and never taking orders from above or preying on those below, then external anarchy would manifest.
Anarchism does not mean chaos but the absence of άρχωνs, masters. To avoid ambiguity the term could newly be coined as an-archon-ism. Anarchy = no hierarchy, at least not one based in falsehood and coercion, i.e. immorality.