Zimmerman was patrolling because he was in the neighborhood watch, not because he had a CCW license. The NW does patrols here too (just moved to Alabama). Don't know if they carry when they patrol, or if they even have licenses, but I'd carry if I did that.
100% agree that a CCW badge has no legal significance and serves no appreciable purpose. From speaking to the many cops I know, or knew before I moved, they consider it a joke too. Many also feel it could be dangerous to give the wrong impression to a responding officer. I personally feel it's a bad idea.
I've been away for a while, but did you just move too? Noticed your username changed.
It's a fine line between carrying any badge and being guilty (and charged) for impersonating a police officer. No good reason to carry a CC badge. You have the permit in your billfold if proof is needed. Otherwise, you're just some wantabe that will eventually get you in trouble. One day I was a cop with a badge; the next day no legal credentials showing that I had been one for 13 years. Don't try to be something that you're not.