I don't think there's any danger of the police helicopter disappearing any time soon. While a UAV can provide some limited service with respect to surveillance, there's a lot it can't do, and even using one for surveillance misses a lot. having a manned crew on board is essential to a law enforcement (and most other) mission(s).
I've seen a distinct lack of ability on the part of the UAV...and I mean the high dollar, best we've got. Their ability to hold a simple altitude has been les than impressive, and there's a lot they miss when performing a routine surveillance mission. When they're working, they work great, but I've seen the results of losing link, or losing control, and I've seen people nearly killed as a result. I'm not impressed in the least.
What is really the point of having a UAV that carries people...making it once again a manned vehicle? Remotely piloting an aircraft sounds wonderful...but if the concept is to eliminate the pilot but leave living, breathing personnel in back...then it's a wasted concept.
Some would suggest that while presently many autopilot or autoflight systems can do better than the pilot in most respects, the autopilot exists to serve the pilot. Likewise, even in a position of automation conducting the flight, such as a remotely piloted vehicle might entail, if nothing else a pilot on board is nearly essential to back up the automation.
I've seen UAV's miss a LOT in an operational environment. The operator is looking through a toilet-paper tube when it comes to seeing the environment below the aircraft, whereas a pilot and crew will be seeing a lot more. A UAV doing a route search, for example, can easily miss an explosion along that very route unless it's looking right at the point of the explosion. A pilot flying a live person operating the sensor package won't miss it because the pilot sees more, uses his periphery, and can look around.
Likewise, a crew on a cargo aircraft has an opportunity to do more with the aircraft. Automation is often used during an inflight emergency, but it's the automation that simply performs basic control tasks while the crew handles the complexities of configuring the aircraft and making the judgement calls necessary to address the problems at hand (both short term, and long term). This really does need a person on the spot, rather than a remote piloting situation. Further, with the demonstrated inability to even hold an altitude, present UAV's offer little more than a hazard to other air traffic. No thanks.