Russell,
Ideas like this always work in theory but the reality is Air Ambulances would have to go from having a pilot and two paramedics to a SAR trained pilot, a fully trained winch operator and a fully trained winchman - rearcrew whose medical skills may be somewhat less than the incumbents. Do you really then have an improved capability?
It's easy fall into the trap of watching videos like the ones posted by TeeS & Brilliant Stuff and think - "I could do that - I'm sure an Air Ambulance paramedic could too". I'm sure he could, after the appropriate amount of training. Training that will come to the fore not on nice days like the ones shown but on sh1tty days where it's all going wrong. Can the Air Ambulance charities afford the 100 hours or so per crew member required to turn them into fledgling SAR crew? Do these charities then have the time and money to devote to ensuring that this fledgling SAR crew have adequate continuation and currency training? These are perishable skills you know. Aviation is littered with the corpses of people who have bitten off more than they could chew and when an inexperienced crew get 'rescue fever' and envisage their names in the papers, common sense doesn't always prevail.
Factor in all the other points about performance, lack of cabin space etc and you'll see that although the Air Ambulance publicity men might get all moist about a proposed winching capability, putting it into practice is somewhat different.