Actually, the best counter example is Afghanistan after the retreat of the Soviet Union. That country's infrastructure, social organizations and virtually everything that we associate with central government and authority had been destroyed, and the country was in anarchy by any practical definition of the term.
According to the "theory", everything should just settle down to Utopian splendor, yes? In actual fact, the Taliban flowed into the power vaccum. Second reality check is Iraq; the Ba'athists were removed and now the Iranians and Wahhabi's are attempting to create chaos and anarchy in order to create the conditions that will allow them to supplant the legal authority of the Iraqi government.
As for Spain, the Ukrainian "Green" movement and the fate of Russian cities under the local Soviets, one reason people finally accepted the imposition of Francoist or Bolshevik dictatorship was the sincere desire for some sort of order to come into their lives (France after the "Terror" was in much the same boat).
Even on a very small scale, most communes set up in the 1960's by the Diggers and Hippy movement attempted to start with some sort of "anarchistic" principles (heh) and where are they now?