[feoren]

Other benefits of reporting it, other than insurance, is that it makes these kinds of statistics more accurate, and that in the unlikely event that they "accidentally" solve the case, it'll be easier for you to get your stuff back. The latter can happen if they arrest someone for some other reason and find what appears to be a bunch of stolen property or something. It's not likely, but it seems like it'd still be worth reporting the crime.

But you make a good point that a lackluster police response does lower the incidence of reporting crimes, effectively doctoring crime statistics. You'd have to evaluate whether this trend has increased or decreased relative to historical periods when factoring that into any comparison, though.