Set constitutional carry aside for a minute.
Backward thinking. People are all worried over CCW. LEOs want to know, and in some states you must tell them, who's carrying. They got it all backward. CCWs have been vetted. CCWs have had real background checks. (NICS isn't a background check, btw, just a list of prohibited persons.)
SO
When a LEO runs a license or plate and it comes back CCW, the LEO should just get on their bull horn: "Sorry for the inconvenience. You were speeding a might. I'll mail you the ticket later. Please don't let me detain you any more. Have a nice day." End of encounter.
BUT
When the LEO determines a person DOESN'T have a CCW the LEO should be suspicious. After all they wouldn't submit, or couldn't pass, or didn't pass a true background check. This time, with guns drawn and numerous backup, "Out of the car. One at a time. Hands over your head. Up against the car. Frisk'm boys."
I'm think states, instead of a maintaining a list of CCWs, should have a list on non-CCWs. After all they're they ones most likely to be criminals.