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.

> If you report a minor robbery to the police in any large American city and you aren't a public figure, there is functionally a 0% chance of them following up on it much less solving it.

I have known people that had stolen things returned because the police found the items while investigating/arresting the thief for other crimes. It seems foolish to not bother with filing a report just because they aren't actively investigating every report they receive.