Nonetheless, your use of an analogy implies that you think there's something faulty to the argument, when it is in fact a completely valid and reasonable argume

Nonetheless, your use of an analogy implies that you think there's something faulty to the argument, when it is in fact a completely valid and reasonable argument. So your analogy is rather toothless/meaningless. If you want to argue that cops are good at their job regardless of how they spend their time, then do that, but your analogy by itself isn't very convincing of anything.