I don't believe the issue is training I believe it is one of environment. The typical armed citizen encounter is between 2, or more, persons in very close proximity to eachother. ID'ing the BG while happening quickly it certainly is positive. In other words the person threatening you is typically ID'ing themselves through thier actions and is usually within 7 feet of you. No need to take much account of environment, no time or room. Just shoot the bastard in front of you.
The typical police encounter involves arriving into mayhem in progress. multiple People running, screaming, perhaps shoots being fired. They must ID the BG(s), take cover, assess the surounding area and return fire (while not hitting the bystanders). Wow, pretty tought circumstances.