The average pilot is not well equipped today to cope with a novel, time critical, highly dynamic event. Much like Chernobyl reactor technicians. Working out what is trying to kill you in the absence of information is a challenge, and those occasions need to be minimised, with crews given training in SA matters.
I would argue that the average pilot was never equipped to cope at any point in history, not just today’s pilot. Pilots are humans and suffer broadly the same natural response when faced with a novel, time critical, highly dynamic event.
The way to mitigate that is to include the human style responses into the training and develop systems to minimize the effect startle factor. Eg. We train for V1 engine failures, but rarely do we train for the bird strike, compressor stall at v1 failure. So the first time you hear the massive bang is when it happens in real life. But look at the reports and videos. The evidence points to this type of failure as a primary way an engine will fail at takeoff. Not just a flameout or fadec rollback.