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You need to define "viable" for the argument to be meaningful.
Nature consists of pure anarchy, and it's viable.
Anarchy is not an economic system, it is a lack of a form of government or leadership. To claim that it is not a viable economic system is a misunderstanding of the term.
How do you know unless you experiment? And how do you experiment when no government in the world wants to give up power? Anarchy could be viable after mass decentralization.
It is important to remember anarchy is not only an economic system, but a political one as well (or lack thereof). It demands the absence of a monopolistic entity which exerts dominance over society through force, as opposed to competitive means.
It is entirely possible to live in a world without centralized rulership, while still having rules and laws governing human interaction. Organization would happen on a voluntary basis, and those who break the law would still be punished either directly or indirectly through economic ostracization.
There is a legitimate form of this. It's called Revolutionary Catalonia. Ancap ideology is ridiculous but not ancoms
Bitcoin is a direct counterexample to that. While it's admittedly on a small scale, it has a relatively functioning currency and economy.
Anarchy is not an economic system, it is a social system. Anarchism is based, in part, on the moral premise that we should not force each other to do things,and that no one has the authority to rule over others.
Several anarchic movement (Spanish Revolution of 1936, Makhno movement in Ukraine, the start of russian revolution of 1917) was quite economical successful in the past. The reason why they failed was mainly military reasons.
Without moderation from a strong institution, humanity is prone to commit acts of savagery and make progress impossible.
Nature is governed by law of the strongest which is basically anarchy
Without organization, men wouldn't have the impetus to create housing and caring for others, leaving the incapable population under misery.