Are you implying that enough people can't be trusted not to shoot at police with their guns that it justifies an armed response to every call everywhere in the entire country?

I think it’s more like if you are a first responder, the math tells you whomever you are dealing with has a gun. That changes the dynamic entirely.

The math doesn't say that - the 120 per 100 figure is misleading: obviously everyone doesn't own a gun. About 22% of people report owning a gun. So yes, a high figure, but the chance of someone owning a gun AND currently carrying it brings that number down a bit. I do agree that it's still quite a dangerous situation regardless.

1 in 5 is still far higher than UK first responders have to deal with.

Well then let's run the numbers: which math are you talking about, the number of guns? My question stands, then. After that, where is the line that changes the dynamic "entirely?"

I‘m not sure whether measuring the number of guns per citizen is a valid measure. Take a look at Switzerland.

I think it goes down with many more factors applying at the same time, not just „guns“.