I have had similar ideas. It seems as though stings such as this would be used more widely. You would think enterprising police chiefs and Sheriffs would do so. Why don't we?
I recall a program done in San Francisco, where they had “bait” people flashing money and trolling for thieves. They caught quite a few.
And I recall that they apprehended the same guy twice in nine months. One can only imagine the hundreds of crimes this guy probably committed during that nine months.