Skyhigh
Let's get back to basics. You don't really know much about aviation or helicopters in particular, so lets imagine we talk about fire engines and ambulances with similar capabilities.
The emergency vehicle can carry 3 people, go for 1hr 30 mins between refuelling, has only 4 petrol stations in the whole area covering 1.5 million people, 1 of which is open at night. Each can do a very small amount of which the other can (firemen: first aid, ambulance crew: fire extinguisher) but don't have the capacity to carry any more kit.
We have two options: base each vehicle centrally to react to the appropriate call, or make each roam about until something happens.
Based centrally and reacting means that they can send the appropriate vehicle to deal with a definite call, they can get there and back without refuelling en-route, and chances are they will have
on average (you'll like that statistical reference) a good success rate.
Roaming the countryside, the appropriate vehicle is more likely to be further away, in need of a refuel (especially at night) or in for a service (this goes by hours operated, not time-scale). The Fire engine can turn up for the car accident when the ambulance is too far away, but they can't deal with 2 spinal injuries or have space to carry the patients to the hospital; the house fire really doesn't need a fire extinguisher......
Let's have a fireman and paramedic on each vehicle, and have both sets of equipment carried, I hear you cry. Well, the vehicle can't carry enough, or if it does then there is only enough fuel space left to drive from home to the petrol station. Each crew member is also of much less use to the other under each scenario. Let's dual qualify each crew member? This may be possible, but there will be a huge dilution of skills and experience. Certainly, the unit is no longer of any practical use and is now twice as expensive, far more ineffective and infinitely more difficult to crew with appropriately qualified staff. The local bean-counters look at the high cost and low results and decide to save all the budget for the old fashioned, but now more efficient methods which we initially tried to improve upon.
Getting back to the Police situation, we can patrol all day, but see above.
Your 3 hours might be for 6 half hour tasks spread throughout the day. Factoring in bad weather, when even if qualified to fly the pilots/crew could not see the ground to help, and servicing, you might have 4-5 multiple sorties per day. Alternatively we could probably patrol for 10 hours a day but still only attempt to attend the same suitable incidents whilst probably not having enough fuel to assist or taking twice as long to attend each. Success rates half, and running costs double (as do servicing costs, time unavailable because of them and the frequency of buying a new helicopter because the old one is knackered too early). Would you buy a 250000 mile taxi or a 50000 mile private car of the same age? Guess which costs more to maintain. Your "poor value for money" helicopter has now cost twice as much to operate and has achieved half as many successes.
I am sorry you are fixated on blaming one service for not doing the work of another, but why blame a fire-crew for not being able to save the lives of a heart attack victim? Or a paramedic for letting a house full of kids burn down when he had a perfectly good fire extinguisher in his ambulance?
Really, I think your concern and somewhat tenacious energy would be better served by campaigning and researching the provision of an air ambulance service and better coastguard helicopter provision in N.I. because one machine will not do both jobs (winching/rescue and emergency medical aid/ambulance). The police have saved several lives as witnessed in local papers if you Google it, but there is little capacity in affordable sized helicopters for multiple roles per cab. Everything in the heli world is a finely balanced compromise.
I hope that this may help you, and I really wish that you could assist in the real problem - provision of a realistic air ambulance for the province (not a rescue/winching pipe-dream). These forums have many knowledgeable people who are more than willing to help if approached in a reasonable manner.
Lastly, I suggest you check the CAA website and download and study the Police Air Operations Manual (CAP612)
http://www.caa.co.uk/application.asp...=detail&id=210
I had a quick look and it may show you the tight restrictions they operate under - more restrictive than commercial operations in many ways.