The problem at the root of this discussion and most all of our other problems is "we are being robbed of more than 99% of our labor's prosperity".
With that problem corrected, I contend that the anarchism/government question would be drastically different. People wouldn't focus on how to stop theft because there would be far less motives for people to steal. If people could earn a fair living just flipping burgers and they could also earn a wealthy living by pouring concrete, most existing crimes of greed would become not worth the risk.
On this site, hopefully, we all know who is robbing us at every link in the chain. I say, all we have to do is offer up better competition to their banking services and to their minions (the mega-corporations') goods and services and then run their stocks into a death spiral. By offering better alternatives, we not only keep the economy going but we foster improvements along the way.
This gets into the how of fixing it, but I think you wanted to focus on whether anarchy beats the other 'isms' in terms of how best to run a society. All I am saying here is that this debate is a drastically different one if we consider how wealthy people would be without a banking cartel taking 99% of our earnings.
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