STANDTO
Looked at logically, I am sure that you are right that there is a better way of deploying helicopters for public emergency services purposes. However, there are two points that occur to me about this:
One of the major problems is that the political vested interests and empires involved don’t want to see beyond the ends of their respective noses. So, with the exceptions of one or two far-sighted organisations like N Wales Police, until there is a major national political initiative you will never get the various purse-string holders to agree and combine their money.
The other thing is that your “bigger, better more of” approach to helicopters would cost a lot more and there are lots of moans already about the cost of these helicopters. There seems little prospect of moving away from relying on the support of charities (for air ambulance) and the goodwill of the military for SAR. Despite the grants provided by the Home Office, some Police Forces still do not have air support at all.