I am not wanting to start an argument (?) but it seems as though CK's answer (supported by crab) is just throw more resources at it and it will be better. Whilst true, this is not much of a revelation. It also ignores the other beneficial ways that you might spend some of that same money, if you could devise an effective HEMS (or police ASU) system leaving a bit of surplus.
The health industry remains unconvinced of the benefit of HEMS anyway (especially in the UK). If there is any spare cash floating around under their control or influence, they will find other ways of spending it. A major initiative to spend lots more money will need some good evidence to justify it. In both the HEMS and police ASU world we have been very lazy about proving our value.
It is also only of limited use to say throw away the current rule book. For the foreseeable future, we have that set of rules (more or less) to operate by.
The current possible/recent upheaval in HEMS is about power politics and asserting train-set ownership rights and has little or nothing to do with effectiveness or efficiency unfortunately.
The peculiar route by which England and Wales acquires its HEMS funding means that the costs of running the helicopter can be funded by means which do not involve an objective review of the value of the service provided. Morally though, we should try and make it as effective and efficient as possible, and be able to demonstrate that, in case anyone ever asks