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.

Plausible sounding theory, but in reality what kills cops is traffic accidents. Even there it's not people running them over. Cops are seldom charged with DUI where other dangerous behavior on the roads.