Whilst I agree it is pointless to do an immaculate shut down procedure and subsequently crash into the terrain, it is important to secure the engine in a timely manner. Once the engine is secured, then subsequent actions can be left until you are clean or later.
I agree with "timely". I certainly wouldn't
delay any critical actions once we had agreed on what had happened and what to do about it. What I don't like is hands flashing around the cockpit pulling knobs and levers mere seconds after a warning has appeared. I included the possibility of leaving drills until clean or beyond on the basis that if it is that hard to determine what's going on, the problem is likely pretty complex and it'd be easy to respond inappropriately.
The previously quoted examples were all uncontained engine failures. It's really not your day if that happens - if you're lucky, shutdown drills may work if shrapnel hasn't cut through anything too vital.
From the 1968 BOAC accident:
...when the flight engineer fully retarded the thrust lever; the check pilot and flight-engineer simultaneously went for and pulled the horn cancel switch on the pedestal whilst the co-pilot instinctively but in error pressed the fire bell cancel button. In front of him the flight-engineer went for the engine fire shut-off handle but he did not pull it.
That looks to me rather like a CRM failure with everyone (including an observer) doing their own thing and the captain maxed out flying the aircraft. Knowing what we now know (of which much has been paid for in blood), if they'd slowed down a bit, diagnosed the problem then deliberately executed a monitored fire drill, things *might* have turned out differently. The same thing happened on the ground: most of the evacuation drill didn't get actioned, which didn't help reduce the fatalities...
I suppose what I'm trying to say is that we shouldn't be rushing critical drills close after the event that caused them, especially when near to the ground, force majeure excepted. Equally, leaving problems that will probably get worse to stew for inappropriate lengths of time is not a good idea, either. Somewhere in-between would be best and it is a fairly wide band; I would have thought that most experienced aviators would be reluctant to take action until they had a fairly good idea as to what was wrong and that the action proposed as a remedy was suitable.