The country was divided and there were many opposing forces including interference from other nations. It is therefore more correct I think to call these examples an "experimental" rather than a "successful" anarchistic society. There are other examples of this in existence today amongst the commune movement I believe.
I also left aside tribal entities since they are quintessentially conservative and traditional societies with well defined hierarchies, rites of passage and governing councils of elders. The endemic conflict amongst competing tribes also argues against calling them an anarchistic society.
The very notion of anarchism is a relatively modern one and although it may hearken back to a more idyllic past in its emotional content it is nevertheless associated with the modern idea of the state since it proposes a departure from that model.
To say "it works beautifully" is I think aspirational rather than actual. There is nevertheless I believe a future society that will be everything we ascribe to the perfectly anarchistic one. That will be the Kingdom of God on Earth when everyone will have the Law of God written on their hearts and minds and will by nature act in accordance with the will of God. The nature of this society will be "righteousness, joy and peace in the Holy Spirit". It is this society I am convinced that is foreshadowed in the longings that humanity has for a perfect society.
"Jesus answered them: 'Truly, truly, I say to you, everyone who commits sin is a slave to sin. The slave does not remain in the house forever; the son remains forever. So if the Son sets you free, you will be free indeed.'" (John 8:34-36)