anarchism isn’t no government, it is (generally depending on ideology) about the abolition of arbitrary hierarchies and power structures, not whatever looney tune idea of total chaos you’ve got going on

Forgot to respond to this. Anarchism absolutely rejects the state, that is what has defined anarchists during revolutionary times and set them at odds with those willing to set up state power. I know anarchy isn't just chaos, there is a theoretical system of government not involving hierarchy, but anarchists have always resisted the establishment of a state.