I get the argument and agree that it would add another layer if there was an understanding all people are armed and willing to protect themselves. I have no idea what the stats are on eg street/home robbery from countries or states where firearms are legal and the majority of people carry. I also know of some areas in eg London that have private security.
I'm not entirely convinced that this anarcho thinking isn't just utopian, I'm just speculating if this would just be lots of inefficient private security instead of a state security. (I get the free market will solve this arguments against this too) but also have my doubts.
I should also add I'm not really against it either tho and it can't be too much worse lol. I'm just slightly sceptical ¯\_(ツ)_/¯