All the problem also applies for pistol. At least a machine pistol carbine can deliver better kill chance up close. There is no need for range because it is a side arm. A rear officer should not go sniping people 300m away.
If they're armed with a pistol solely then the threat level is low and for those they must deal with, the pistol is more than ample. It's compact, easy to handle, easy to maintain, light weight, less threatening looking (as in not appearing over kill) perfect general all-round weapon. And in certain cases not killing the suspect can lead to a capture which can be infinitely more useful in the long run than a dead suspect.