If they're not reported, how do we know that they're seriously underrated?
I have talked to numerous people who have lived in bear country and who had numerous encounters with brown(grizzly) and black bears. Nearly all of them tell me warning shots work most of the time, and there is no reason to report them to the authorities.
So, there is a lot of anecdotal evidence both about the success of warning shots, and the lack of reporting.
In addition, the authorities in the Svalbard Archipelago require warning shots and or flash/bang "bear banger" fireworks. For aggressive and/or curious polar bears.
Similarly, in their literature they claim warning shots work most of the time.