They do at the scene of the fire, and EMS leaves their ambulances running on scene as well. Cops leave their cars running while out and about, and usually off if they're parked at the station.

More to the original point though, I've never seen cop cars, fire trucks, or ambulances idling at their respective stations. Not a clue what SOOP sees in his area.

While I certainly agree with your overall point, I'd guess that firefighters have someone who's job it is to start the engine/truck while their fellows are donning their gear.