My CHL instructor was a long time LEO now retired. I've taken several classes with him since 1995 (new license and renewal). Every class he always goes over when you are required to show your CHL. He said of course that it isn't required if you are not carrying, however, he recommended that you always show it. Main reason...it shows you are a good person that has passed background checks and so on.
I suppose the other reason may be the just in case you forgot. He's always suggested that if your wife doesn't have a desire to carry, she should still get a license to cover the event that you left your handgun in the glove box or some place that your wife doesn't end getting in trouble.
I've only been pulled over once when I was carrying and that was just when TX CHL was in its infancy, probably late '95 or '96 and because it was new a lot of LEOs didn't know how to deal with CHL. In my case, I rolled down my window, put my hands on the wheel and told him I was a CHL and had my firearm on my hip and waited for some instructions. Since my wallet was in my pocket close to my gun he suggested I get out of the car. I think I just showed him where the weapon was and then he had me pull out my wallet with my DL and CHL....and all was good. Still got a ticket though.
Other times when not carrying and stopped by LEOs, I handed over my CHL. They asked if I was carrying and I answered no and he handed it back...no harm, no foul.
What is interesting now is that the past legislative session CHL is now a valid form of ID. If you voted in these past elections you could have provided your CHL as valid ID. I would assume that if stopped on the sidewalk by a LEO, you could present your CHL (even if you aren't carrying) rather than your DL to provide ID to the LEO.