Maybe this will help with your questions, too, since litters were mentioned.
IMO. Optimal is helicopter recovery, if the site makes landing or pickup possible. It's more discreet, there's a lot less risk to personnel (and you need fewer)*, and there's a lot less psychological trauma to the folks involved in the recovery. Also, I think of it as keeping our armed forces prepared for military activities (e.g. downed pilot extraction) or large scale search and rescue (e.g. earthquake). It's about emergency and military readiness. Helicopters and SAR would otherwise have to be training with pretend victims and mock situations; they might as well be getting practice on the real thing. Military helicopters are often used for recovery and SAR. IMO this is tax money well-spent (except in cases where tired climbers expect courtesy rides; yep, this happens). Just getting the timing right for a pilot to land and the team to load the litter (and avoid the rotors), takes a lot of coordination; it sometimes has to happen very fast.
Note: some helicopter recoveries are super-high risk, and take inordinate skill. These involve a cable being dropped from a helo in an area where the helo can't land, e.g. at the bottom of a slot canyon or off a craggy shore in the ocean. I doubt this case is one of those.