Yes, I think there is a point where the definition breaks down: either at the individual level, the family level, the extended family, etc. I’m going to reluctantly link one my very first posts here, talking about definitions.
Words tend to break down at the boundaries, because they were coined in a certain context and were never intended to be used at the extremes. I basically just define anarchy as the lack of a territorial monopoly ala Long’s definition that Sage posted above.