> Is there some sort of wide-spread belief that the world works like an episode of Law and Order and every crime is instantly solved by rolling up your sleeves and doing good old fashioned detective work?

There is to a point, and it's not some random organic sentiment: this is the image that has been crafted for decades, if not centuries. The police has a role in pushing it, but it's also has been a useful fiction for our societies as a whole.

"crime will somewhat get punished" has more weight with a competent agency with at least average intelligent people.