You seem to be suffering from two misguided assumptions. First, you misunderstand the role of the police in our society. Second, you are setting up a false dichotomy.
The police exist to provide the illusion that if you commit a crime, you will go to jail. As long as would-be criminals believe that if they break the law, they will be caught and punished (or at least, that there is an unacceptably high likelihood that they will be caught and punished), they have an incentive not to commit the crime. When you leave a
"low-hanging fruit" crime unpunished, you are telling criminals that they can get away with crimes, as long as they aren't murder, rape or kidnapping. That's got Bad Idea written all over it.
While I seriously doubt that anyone on
/. is going to argue that the alleged theft of a cell phone (even an eagerly anticipated prototype cell phone from a well-known company with bajillions of eager fanbois) is more important than a murder or rape, it's just plain stupid to argue that all cops should only work on murder and rape cases until the backlog is gone. Think about it for a second -- next time you get in a car wreck or you find someone breaking into your house, do you want the cops to refuse to investigate the accident because there is an unsolved murder that the
entire freaking department is working? You will end up with anarchy, and I'll wager that the rate of murders and rapes would skyrocket because the criminals know that the po-po won't respond to calls because the murder and rape cases on the books are "a higher priority" than a simple breaking-and-entering call. And, every once in a while, a seemingly low-priority case ends up leading to the arrest and conviction of a big-ticket criminal.
The police department must try to strike a balance. When a crime has potentially been committed, they
have to investigate -- even the lower priority cases -- because it is impossible to solve every crime...but as long as a reasonably high percentage of them are solved, it is more advantageous to most people, most of the time, to obey the law.