What if ...
The cops responding & arriving to a shots-fired/man-with-a-gun call think they see:
Someone holding a "gun" in a threatening manner, only to later discover it's a cellphone, pack of cigarettes, tape cassette, cassette recorder, video camera, screwdriver, beer can/bottle/glass, flashlight, etc., etc.
Someone holding & displaying an "assault weapon/machine pistol" in a threatening manner.
Someone holding some sort of unidentifiable firearm in a threatening manner.
Someone holding a suspected firearm in a threatening manner, who doesn't respond to verbal commands to drop the weapon (pick a reason ... some combination of sheer fear, distraction, injury, tunnel vision on a perceived threat, auditory exclusion, etc., etc.), and who appears to be threatening another person with it while disobeying the shouted verbal commands of the arriving cops.
Someone holding & displaying a firearm, but can't see the L/E badge in the person's pocket ... or the CCW license ... let alone the immediate reason the firearm was presented, and perhaps used, in the first place ...
Someone holding a suspected firearm, and then at the same time think they hear a gunshot(s).
Someone holding what appears to be a pistol make/model with which they're familiar, only to later discover that it was a replica, airgun, etc., etc., and the person holding it had been actively engaged in some "realistic" role playing-strategy gaming, horseplay, etc., etc., and which wasn't immediately apparent to the responding cops.
You just don't know ...
I remember the time I was the first unit on the scene of a reported jewelry store armed robbery. I learned that the R/P Victim hadn't waited for us to arrive, but had grabbed his own handgun and run out of the store, chasing the suspect, who was also armed with a handgun. Both were Hispanic males of similar description, dressed in similar non-distinctive clothing (forgot the clothing details these many years later), and apparently were both last seen running down the street, with guns in their hands, in a neighborhood of predominantly Hispanic residences and businesses. You can bet I quickly got on the radio to warn the other responding units of the potentially confusing similarity of the pair of excited, armed fellows they might discover running down one of the other streets.
I wouldn't presume to offer other folks advice who I'm not responsible for training ... seek it out from trainers, instructors and sources you trust ... but you can bet that one of the things that's always on my mind when I'm working plainclothes inside the jurisdictions of other L/E agencies on a daily basis, as well as when I'm off-duty on my own time, is that as far as other cops are probably going to be concerned (if something occurs which makes me feel compelled to present my weapon) I'm potentially just another "man-with-a-gun" until they've otherwise identified me after they arrive on the scene.
I've gone out of my way, when talking to dispatchers on my cellphone and/or radio, to belabor my detailed description and status when requesting the response of both units from my agency (lots of new folks whom I don't immediately recognize under non-stressful conditions, and vice versa) and other L/E agencies when requesting assistance.
I remember one instance, when I was wearing more "casual" plainclothes for a detail, and one of the responding officers from another agency kept commenting that I just didn't look like a cop, which is why I had my partner meet them at the door, since he was dressed in more conventional, more "formal" plainclothes. The fact that I was wearing a badge on a chain around my neck, with an issued ID card inside the badge holder, didn't seem to reassure that officer much for some reason ...
I also agree with the comments that some cops are unable to identify their own issued weapons, and sometimes have trouble recognizing such differences as semiauto/revolvers, stainless/blued/black finishes, etc. ... and that's under ideal, well-lit, non-stressful conditions, too.
The decision of which concealable handgun to lawfully carry, as a legally armed civilian/citizen/member of the public/non-LE (whatever floats your boat), unless restricted by local law or license restriction, is probably a personal one ... and best determined by the affected individual, making an informed decision after the appropriate research relating to his/her preferences, anticipated needs, restrictions, skills and experience, etc., etc.