I suspect this fear of guns largly explains the additional risks police face.
assuming everyone has a gun and is willing to use it, raises the stakes of every encounter. so instead of a police encounter starting at a very low risk level (casual conversation), it starts a very close to deadly force risk.
This causes both sides to be a lot more tense, with a lot less room for mistakes. It also makes any encounter feel very risky.
I don't think people having a gun prevents police from starting an encounter at a casual level. But the assumption everyone is out to harm them, and has the means to do so, does.