A prop is worth half a page of exposition. If you take out of your raincoat pocket a Mounds bar, and then the next time you take out something equally puzzling, when you take out the next time the gun, you've already captured the audience's interest, because they were surprised by the first two things. That's the kind of thing I would be dealing with, to find some way to always have a prop, as opposed to words... That's one of the reasons I would sometimes reach into my pocket and pull out a box of Raisinets. Or another time I might have salt and pepper, and in the other pocket I'd have a hard-boiled egg. And then finally I'd pull out something that actually had something to do with the case.
The one thing that always bugged me about Columbo is that Columbo often wound up nailing the murderer on incredibly flimsy pieces of evidence ("How did you know he was in his gym clothes if you didn't change his clothes?"). I guess that's part of any mystery show, but somehow it always seemed worse on Columbo because the murderers, being such ruthless Rich Guys, seemed like just the kinds of guys who could hire a good lawyer and make hash of Columbo's crackpot theories. I recall MAD Magazine did a parody of Columbo where his superior complains that Columbo always goes after the rich guy instead of the obvious suspect, gets the rich guy on some tiny piece of evidence that can't hold up in court, and then the department gets sued for false arrest. But instead, supposedly ruthless dudes like Jack Cassidy and Robert Vaughn crumble to pieces when Columbo says "uh, just one more question." Wimps.