"What type of system would you propose anyway, other than capitalism and lawyers to resolve grievances?"
Under anarchism there is no centralized authority (government) so how do you maintain order and provide restitution for injustice? Not the only alternative... but the default would be "mob justice" which can be seen as a collective form of vigilantism. I doubt any intellectual anarchist would advocate for this, however it's a problem they would need to solve.
I'm sure that alternative solutions have been proposed however here we have a pragmatic problem. Such systems by necessity require acceptance of ideology by the public at large. Without government (and state force) there is no way to impose this from the top down and as such its an uphill battle - you would literally need to convince the majority of people that your (esoteric) system was the correct one. Such a system would need to compete with the natural mob mentality of humans - and do so without any authority keeping the system in place. I can't see this happening in the real world.
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