But then you wrote this.
"Now, I take it back. It is possible, but only in one scenario. True anarchism won't result upon the collapse of the state. It will be the result of society's transcendence beyond the state. As society progresses, becoming more and more educated and experienced, it will need the state less and less. That is, at some point that cost of being educated and providing stability will be less than the cost of repression - and everyone will know it. The state will shrink as pressure is brought to bear against state intervention as participants will know this intervention to be more costly than not. At some point, the state will shrink to nothing. Perhaps it will remain as a curious tradition, much like many old monarchies."
Education and experience has not brought us any closer to anarchism and will not unless anarchism is mandatorily taught in school but that is oxymoronic to the anarchist ideology. I'll go one further and say that "education" has distanced us from anarchy. The state doesn't shrink but they do tend to fall abruptly when they get too top heavy but then again at best you will get a short lived period of partial anarchism before the next government arises.
A new government will always arise and people may look at the old as a curiosity, perhaps, but they will still be under some new government. Anarchy doesn't work for two simple reasons. First you would need complete participation/nonparticipation for an anarchist society to exist. Secondly without the complete participation you would need some form of government to enforce anarchism which again is oxymoronic.
The problem I see with a lot of ideas that look good on paper is that they require some form of mass enlightenment of the human race to one way of thinking which will not happen. You will always have different classes, different incomes, different ideologies, etc...
Anarchism will never work as a viable long term societal norm.