It's physically impossible to solve most of those "hard" crimes. No evidence, no witnesses, no recordings, no leads, nothing. Reality precludes the possibility

It's physically impossible to solve most of those "hard" crimes. No evidence, no witnesses, no recordings, no leads, nothing. Reality precludes the possibility of them being solved. They're also not allowed to mass read text messages, listen to phone calls, get phone-call "metadata", run security-camera footage through "AI", do facial recognition, can't capture everybody's biometrics, etc. Oh and they can't profile people or perform stop/frisks, their hunches are biased, they can't walk dangerous neighbourhoods because they then "police" them unfairly, etc. They can't win. At this point, short of magic and wishful thinking, I don't see what we want the police to actually do to solve these crimes. No wonder they "game their numbers" as you mention, that's all they're really allowed to do by us.