If my state law does not require me to tell you about my gun or permit, why would I? It is a legal object in my lawful possession. The safest place for my gun is in it's holster with nobody touching it. You, as a police officer, may feel no need to fondle my gun when I tell you about it, but can you guarantee that 100% of the other officers will not want to?
When I tell a police officer about my lawfully possessed and carried gun, which is safe in it's holster with nobody touching, I am doing NOTHING in reality to actually MAKE anyone safer. All that I am doing is extending an invitation to the officer to fondle my gun, uneccisarily, if they choose to do so.
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Before someone asks what do you have to lose by informing...like I said, the safest place for my gun is in it's holster with nobody touching it. Telling the officer about the gun when not required does NOTHING more than extend an invitation to that officer to fondle that gun, "for officer safety", of course, which instead puts everyone nearby at an increased risk of a negligent discharge.
Although we are required in SC to notify an LEO of our CWP and whether we are armed when ID is requested, I think it's a dumb law too. It's almost never relevant to the purpose of the stop, and leaving the weapon holstered in my possession is without doubt the safest course of action. I don't disagree with a word of your justification for not notifying, but I can answer your question of why one might do so anyway.
I respect LE, and I'm one of the good guys. By providing my CWP and declaring my firearm, I convey these sentiments to the LEO. So while I object to the law on 4th and 5th Amendment grounds, it doesn't have much practical effect for me. It's just a dumb law, because the good guys don't have anything to hide, and the bad guys aren't going to tell on themselves anyway.
To your point about whether notifying an LEO about my CWP and firearm invites unnecessary fondling, I've already stated that I agree it's far safer holstered in my possession. I also agree this is a valid reason for choosing not to notify the LEO, where such a choice is legal. However, I would generally choose to notify anyway, even if I weren't legally bound to do so, based on a subtle risk vs. reward equation:
Most officers know better than to remove a citizen's legally carried firearm "for officer safety" during a simple traffic stop. Although it could happen, it's not the expected outcome. On the other hand, by notifying the LEO of my permit and firearm, and thus genuinely and politely letting him or her know that I respect LE and I'm one of the good guys, I may be let off with a warning. In my estimation this is a far more likely outcome than having the LEO remove the firearm from my possession, however briefly. If I thought a more unpleasant outcome were likely, I would not be as willing to notify, but may consider doing so anyway as a matter of respect (again, if not already legally bound to do so anyway).
But to the main point...we should not be required to notify. It should be a matter of discretion for both citizens and LEOs: for citizens, whether they want to notify or not; for LEOs, whether they think they should ask about firearms or not.