The single case of theft I personally know about ever being acted on by the police, was when a business owner spotted the van that’d been present at burglaries of his business and several others (several of them had footage of the van, the thieves, and legible shots of the license plate—cops didn’t care), called the police to report it, and, when they still acted reluctant to do anything, said “you better come down here or I’ll confront them myself”.
I assume what got them to show up was that they didn’t want the bad press if the dude got shot.
Not bad strategy. Though I can see, depending on their disposition them turning against you. "Oh, you have gun? Better not reach for it! Is it registered, where is it?". They could turn into assholes real fast if they feel like you're trying to force them to do something.