Interesting proposition I guess the only reason with SAR being traditionally supplied by the MOD is that historically they have been the only organisation with the resources. Of course the services had a vested interest to ensure that those in peril were rescued as soon as possible - apart from the desire to get you back to work its an implicit part of the contract that you will be backed up.
Now of course teh world has changed and cost is king now - all else falls to arguments of costs. I can see teh new rotary SAR service working but I must admit I would have my doubts on the viability of a voluntary service as you described Leon - just would not get the crews (air or ground) to man it I believe. Not sure I would want to rely on it either.