Just guessing, but don't the city, county, state and feds reimburse people for this kind of thing? In other words, why should insurance companies pay when homeowners can easily, and almost always successfully, appeal directly to the parties responsible for reimbursment? Again, just asking. I don't know it's true. I just get that distinct impression watching Dirty Harry. :-)
I don't know about all jurisdictions, but in cases I know about personally, damage inflicted "in line with official duties" was NOT recoverable.
The worst case which really sticks in my mind: Several businesses were shot up by cops during a "shoot-out" in rural northern CA, and damage claims were refused.
Incidentally, the wanted bank robber didn't fire a shot. He was crouched behind a bus bench at the side of a store, holding a gun to the head of an elderly local man whom he was holding around the neck with his other arm. The cops also managed, in the course of expending over 150 rounds, not to hit the robber even once...but hit the hostage in the neck, shoulder, and groin. The robber threw his gun down & surrendered.
The freezers in the store were ruined; shelf goods were destroyed; the motor of ice-house on the opposite side of the store was ruined; the front windows of another market, cafe, and gas station, and mini-mart across the road from the store were shot out. The 75-100' side of the store was stitched from one end to the other, and as high as 8' off the ground. The cops were behind their cars within TEN TO FIFTEEN YARDS of the robber's position, using pistols, rifles, shotguns, and at least one full auto AR...by a sheriff's deputy NOT authorized to have it.
Incidentally, Jinks, the 70+ YO father of the store owner, who was the hostage, did eventually fully recover. Miraculously, though all the businesses had customers as well as employees inside them, Jinks was the ONLY person wounded.
The various business owners had to fight it out with both the insurance companies and the FBI, CHP, and Shasta County Sheriff's Department, as all of them denied legal obligation to pay damages.