I hope Instructors, Captains, and Mentors have passed on the very most important Trait of a Pilot during Emergency Operations....."THINK!", "FLY THE AIRCRAFT", "NAVIGATE".....then One can deal with Emergencies, Checklists, and Procedures.
The example I use is Bell 212/412 Single Engine Failure.....shy of a Catastrophic Engine Failure (say a Powerturbine Wheel coming apart and sending shrapnel about the place...and starting a big fire)....if One did nothing but fly the aircraft and ignore all the switches and affected engine throttle....thus not making the mistake of shutting down the last remaining engine by mistake....what would it matter in reality.
Being Slaves to Procedure can kill you too!
Prime example of that was the American Airlines DC-10 crash at Chicago after the engine departed the wing. The Crew applied the procedure called for by their SOP....reduce airspeed to gain max rate of climb. Never mind it was a stark clear beautiful day and there were no obstacles in front of them that demanded the extra rate of climb that provided. They did not know the engine had taken out the leading edge devices on that side of the wing.....and that the aircraft would stall and roll over to that side because of that damage. Had they accepted the rate of climb they had...maintained their airspeed....they would be here today.
Never think the EP's cover all possibilities.
Two very Senior TRE/IRE's I know learned that lesson despite being told their SOP for Engine Problems after LDP did not do so. Fortunately it was a 212 Sim they crashed.