I think you just fundamentally misunderstand human nature, the criminal mind, and the overall practicality of running a criminal enterprise even if you assume well-informed rational actors.

If you get burglarized, your ham radio equipment probably won't get stolen. And if it does, it's a crime of opportunity, not because someone found you in a database and somehow knew you had the good equipment.

But sometimes criminals are desperate for guns, or the quick cash that guns can bring. You don't want desperate, potentially violent criminals finding out that your house has exactly what they are desperate for.

If they want the cash, they could even prearrange a fence based on the database search. That's a little too convenient.