Arguing government should be smaller is not the same argument as arguing there should be no government, so using the word anarchy to describe a plan for less government is nonsensical.
Looking at historical examples can lead to a lot of wrong conclusions, if you don't look at the whole picture.
Taking the Wild West as an example, I guess you forgot about the US Army vs the Native Americans, the US Marshalls, the railroads and land grants, the Panama canal, the geographical surveys, the mine claim agencies, the non-federally guaranteed banks which frequently absconded with everyone's money, the federally funded dams which enabled the expansion that exists today, without those the West would still be a backwater, not one of the most powerful economic regions in the world.
Looking at historical examples can lead to a lot of wrong conclusions, if you don't look at the whole picture.
Taking the Wild West as an example, I guess you forgot about the US Army vs the Native Americans, the US Marshalls, the railroads and land grants, the Panama canal, the geographical surveys, the mine claim agencies, the non-federally guaranteed banks which frequently absconded with everyone's money, the federally funded dams which enabled the expansion that exists today, without those the West would still be a backwater, not one of the most powerful economic regions in the world.