There's a big difference between "solves every crime" and "is effective at solving crime". I think you're grossly overestimated what the police will do for you, if there isn't low hanging fruit, or some driving factor (someone "important" involved, multiple complaints, politics, ect.).

If there's single victim that hasn't died and the perpetrator isn't easy to find, they might just wait until they run into them or they murder someone. That's not an exaggeration, I've personally seen them unwilling to step in when a violent criminal is out to get someone, or someones being blatantly defrauded.