The use of military assets for an essentially civilian task has to be asked for by someone outside MOD, and is normally done only where life is at risk or there is no other means of achieving the task. As I understand it, the C17 is on standby for an aeromed task as it is able to fly very sick people in what becomes effectively an airborne intensive care unit. We have Afghanistan to thank for developments with that capability. By the nature of that task, you must have a careful assessment of casualty needs before you embark on it, to make sure you have the right staff and equipment on board (eg you don't fly someone who might require surgical intervention in flight without taking a surgeon with you).
Tragic though this case is, the mass evacuation is currently voluntary and the immediate threat of further violence would seem to have receded somewhat with the death of the individual concerned. The commercial operators are acting as they should by bringing people home as fast as possible, and this has been going on since Friday. This actually an FCO responsibility, as is the repatriation of bodies.
Could the UK have responded faster? The FCO and consular teams were on the spot very quickly, it just didn't make the news. And sending military air assets also requires diplomatic clearance which, as the Nepal experience showed, can take days or not be forthcoming at all. This is where the RN has an advantage, because free passage of international waters allows ships to move wherever. I expect we can all cite examples of the RN diverting ships towards the latest trouble spot. In fact the duty frigate is probably en route right now...
As for expectations of government or military support, it is entirely reasonable to expect rapid consular assistance anywhere in the world. But unless the circumstances are so dangerous or difficult that there is no civilian option, use of military assets should be a last resort and we should not expect it. Nor should we as taxpayers be required to fund the necessary readiness state.