I think the trick was missed years ago - probably as an earlier cost-saving measure. Being an old bugger, when Teeters joined there
was deployed SAR. OK, we weren't an expeditionary air force
per se, but many (relatively) fast and pointed things were stationed or regularly visited overseas locations.
Hence SAR flights or squadrons in the late 60s/early 70s in Hong Kong, Singapore, Aden, Sharjah, Bahrain, Cyprus, Libya (yes, really!), British Honduras etc. In short, where there were RAF fast jets, there were RAF SAR helis.
And we mustn't confuse
Combat SAR (which is really an SF role) with
Deployable SAR.
Professional SAR on the spot is what the FJ jocks deserve. (Yes I know "all SH crews get SAR training" but it's not the same - and I speak as an SH bloke meself). To be bold, might it have made a difference to the ditched Lynx in Bos a few years back??
Should it happen? Very much yes.
Will it happen? Almost certainly not.