I would suppose that LEOs would much prefer to be told in advance that there's a gun present, rather than finding out the hard way if things go bad. Plus, the CHL holder passed thorough state and fed criminal background checks at the time of their application, so there's that too.
If you're a law abiding citizen to begin with, that should never even be an issue.
That being said, I've only ever had to show my CHL twice. The first time, he asked where my gun was, and it dawned on me it was in my pack as I was going hiking. The second time, I tried to hand it to him, and he literally told me, "I don't need to see that."
The first guy gave me a warning and was a State Trooper. The second guy was a motorcycle cop, and wrote me one hell of a ticket.