For anarchy naysayers, look to the Territorial West in America.
There were more bank robberies in Dayton, Ohio in several years than there were in the Territorial West over decades.
No, the Territorial West wasn't purely anarchist; but, it was pretty freaking close.
Most of the famous outlaws who are depicted in Westerns were actually active in the American East. As an example, the James Gang never operated in the Territorial West. They operated mostly in middle America which had already established statehood.
Butch and Sundance did operate in the Territorial West; but, they only did so for a while before moving South of the border.
The Territorial West actually did a great job of maintaining order with no government. A bank robbery in the area was mostly suicide because everyone had a gun and the vaults were well protected. There was actually a spike in murders in the Territorial West after law enforcement was implemented.
The West wasn't so wild.