They should. Of course those are two different questions:
1. Should you and is it important;
2. Do most people in emergencies?
I agree those are two different but interrelated questions. I personally believe the answer to 1 is "yes". On 2 I'd probably have to weasel and say "sure, some do but probably not as many as should".
This is one of the areas in which I think the integrated team diving / DIR / GUE etc. people are 100% right. If you don't train regularly for dealing with problems, you're not very likely to be able to deal with those problems if they arise. If you do train regularly, there's a reasonably good chance the training will kick in even in the face of panic and disaster and help push things in the direction of a better outcome. Further, that training can in itself be rewarding and even fun so there is every reason to do it.
As you well know from your own work, this is why pilots, medical people, security personnel, and those who work in many other fields involving risk spend seemingly disproportionate amounts of time and energy preparing for events that they could reasonably believe might never happen. I actually started to think my little podunk hospital was overdoing it when they put a decontamination unit in the new ER and spent tons of time with mass casualty drills out in the boonies. Then last week a local ball bearing plant exploded due to a nitric acid reaction and 14 towns had to dispatch first responders to the scene. All that training kicked in and the scene and ER ran like clockwork. Many of the personnel involved had spouses, parents, and children working there and were frantically worried, but the training took over and everything worked the way it was supposed to. Everyone survived and got the care they needed.
My opinion is that scuba diving is one of those areas where things rarely go wrong but where they can go disastrously wrong at times. From my first day of class in 1980 to now, part of diving for me has been doing drills to prepare for some of those events. It turns out that the most dangerous thing ever to happen to a member of my family while diving wasn't something we'd ever drilled for, but my son in his mid-teens (whose life was the one endangered) was able to respond calmly and think through what needed to be done even while events were unfolding at breakneck speed.
At one point or another, we've eventually needed to use every skill we've practiced, from swapping masks underwater, to buddy breathing from a single regulator, ditch-and-don at the bottom, CESA due to regulator failure, rebuilding a BCD power inflator at depth, etc.