The police aren't going to be looking on a list of registered craft in an area. They will be looking at the registration number on the craft or what's left of it. If there is somebody they catch flying like an A-hole and their copter isn't registered, they can hand out a nice fine and possibly confiscate the drone too.
The main reason is that registration means that they can track back the owner if they collect the drone at an accident site. It's the same reason that cars were made to have number plates on and be registered. Something happens and they know who to go looking for but they don't pinch everybody in a 6 block radius that owns a white 4-door Ford because a witness to a crime says they saw one tearing away.