Earlier quoted context omitted.
It's very similar in holocracy: the people who are natural leaders will fill the management needs of the organization; it's just more chaotic, less predictable, and not as good. The lack of structure brings out the worst in human behavior. In my experience, it is a horrible system in which to exist. It's highly ignorant of psychology and behavior theory almost intentionally, and it creates far more drama and politics…
Are you speaking from experience? It seems that if you completely do away with job titles, the politics would go away right?
Honestly, my experience has been that structure is one of the key things that makes teams effective (not structure as in "rigid meetings/etc", but structure in the sense of "understanding what their role is and where they fit in")
This doesn't strictly require managers, of course, but self-organization rarely works out that well either as the org gets larger (you have the same problems, they are just hidden and nobody is accountable) :)