If you did that and a cop saw you were about to shoot someone, wouldn't you risk getting shot up by the cops?
Sometimes good deeds get punished.
I believe a Cop would draw his weapon and order me to drop mine before firing. Hopefully he's got good lungs and the rest of the noise doesn't drown him out.
Anytime you draw a gun, you have the risk of someone mistaking you as a bad guy. You're not in uniform, so you have to be aware of what people around you are doing.
There have been CCW holders trying to stop a bad guy who wound up getting shot dead by Cops. If you ever discharged a handgun without hearing protection, you know there's little chance of you hearing the Cop behind you yelling "DROP THE GUN!" That's exactly what happened to one CCW I read about.
Use all your senses. Look around you. The guy you are shooting at may not be the only threat.
When I bought my ID holder to put my CCW permit in, I was just wanting a double-windowed case for license and permit together if I ever need to show to LE. That's when I saw all these "CCW Badge" cases you can buy that have a real-looking badge inside. It's supposed to be so you hang it on your belt, in a shirt pocket, or with a lanyard around your neck. If you draw, the Cops may hold their fire if they see a badge. After some researching, I decided against it. One more thing to have to deal with if I draw.