Not just big cities, but anywhere. Once criminals, drug addicts, or a guy down on his luck for a period of time, in any large, small or rural area knows there is no law, all hell would break loose. Or criminals would come from the outside to prey on the week.
People will abandon those cities then. I could be generalizing but those in the suburbs and rural areas would be armed?
Well without law enforcers the good guys can quickly wipe out the bad guys without fear of going to jail.