I’m willing to give the cops the benefit of the doubt, but at the same time, I’ve always thought that people expected to use firearms in the course of their job should be trained extensively in their use. As others have said, cops tend to be very busy as it is, so I don’t know how they would make this work other than to make it a point-blank requirement and tell them to make it work (that’s how we do things in the Air Force, actually).
Others have said a lot of this, but I’ll throw my loose change into the fray:
“No kill like overkill” - The way we are trained, and I assume police officers get similar instructions, once you have decided that lethal force is necessary, it is your duty to employ it until the threat is dealt with. If the guy with a gun (or a knife, or whatever implement he has that you judge he has the capability and intent to deal lethal force with) is still on his feet, you keep shooting until he is down. You don’t try to shoot the gun out of his hands, or kneecap hip to incapacitate him, or any of that other John Wayne bullshit. You aim for center of mass to get the best chance of actually hitting the bad guy and not a lamp post three blocks away.
That said, police officers are typically equipped with a variety of tools and training to try and deal with a situation before it requires lethal force. Talking down the suspect, pepper spray or batons (or heavy flashlights in some cases, which work just the same as batons), tazers, and finally guns. You use the appropriate level of force for the situation you are dealing with. A kid grabbing a purse and taking off down the street probably doesn’t warrant the gun, or even the pepper spray. A belligerent unarmed drunk, however, will probably get sprayed if he doesn’t cooperate. He probably won’t get tazered or shot unless he pulls a weapon.
On that note, there are a wide variety of things which can kill a person easily, and they aren’t all guns. Knives, baseball bats, etc. can all easily lethally wound a person in seconds. If someone is coming at you or another with the capability and intent to deal lethal force, you do what you have to do to preserve life and limb. So no, a cop will not and should not resort to his gun first if he is equipped with a gun. That’s why he has the whole bat-utility-belt full of things like radios, pepper spray, Mag-Lights, batarangs, and night sticks.
Unfortunately, if you are in a situation where someone might have the capability and intent to use lethal force, you probably don’t have a lot of time to come to that conclusion. Maybe the guy planned to try to shoot his way out, or to commit “Suicide by Cop”. Maybe he was just hopped up on bourbon and sudafed and didn’t realize he was still holding the gun. Hard to ask him now, but if he was going for Option A, we might have had a dead cop to add to the list of gunshot victims. It’s a shitty situation to make a snap judgement in, but once you’re in that situation, you can’t often defer it to someone else.