Bolkow - hopefully you now understand that when you see the Sea King from Chivenor doing what seems like simple tasking that could be done by an air ambulance - it is because we are either the best asset for the job (based on the details of the initial 999 call) or the only available asset for the job (air ambulance tasked elsewhere).
Many times that we end up landing on a beach to pick up a casualty we have actually been launched because the report was of a person in the water/capsized dinghy/surfer etc) who the air ambulance cannot assist. By the time we get on scene the casualty has often been dragged from the water but still needs urgent medical assistance and rapid transport to hospital. To a casual observer it looks like an overkill response but better that way than to send an AA only to find the casualty still needs winching.
Your answer might be to fit winches to AA but that has so far proved to be a non-starter in UK for many reasons, not least of which is their non availability at night except into prepared sites (we can go anywhere - within reason - anytime). SAR helicopters are expensive whichever way you cut it and having more, smaller ones does not provide the economies of scale you are expecting, not least because then you need more crew who have to keep their skill-set with lots of training (and that costs loadsamoney).