Sorry Sam1911 I'll be sure to quote your whole contradictory sentence next time.
Excuse me? I find no contradiction in the sentence I wrote. Enlighten me.
I see the usefulness in the TRB drill, but my point is that I don't see it as an excuse to not look at the gun first and see what the problem is, as some people seem teach.
First of all, looking at the gun isn't very useful. It can tell you if you have a stovepipe or a failure-to-feed or such (NOW can we go ahead and TRB?), but it can't tell you the whether your hammer fell on a dud round or the mag wasn't seated fully and no round was chambered. You look and you see the gun is in battery and the hammer is down. What do you do next? Second strike? On a dud? Great. Maybe it goes off. Maybe it doesn't. (NOW can we go ahead and TRB?) Or did it fall on an empty chamber because the mag was slightly unseated? (NOW can we go ahead and TRB?)
So I suppose you should really take more than a second to peer at the gun and figure out what went wrong. Turn it over and look at the mag. Is it seated? Looks like it. Well, then -- I probably have a dud. Let's roll the dice on that again! Now, what were we doing here? Oh, right, I'm in the middle of a gunfight!
If you practice malfunction clearing the way that most accomplished shooters and trainers appear to teach it, there is no time wasted in looking at the gun and trying to comprehend WHY it stopped. Who cares WHY it stopped? All you need to comprehend is "click." The response to "click" is Tap-Rack-Bang. That gets your next shot downrange fastest -- in the majority of failure cases.
It doesn't matter if the round was a dud -- Tap-Rack-Bang.
It doesn't matter if the mag wasn't seated -- Tap-Rack-Bang.
It doesn't matter if the round was out-of-spec and the gun didn't go into battery fully -- Tap-Rack-Bang.
And so on. The beauty of the system is that you can do this MUCH faster than you can do a visual inspection and assess which solution to apply. (You're probably going to disagree with that, which is fine, but those who study these things say it is true.) You don't take your focus off the threat. You don't stop and ponder why your gun stopped. You just Tap-Rack-Bang, running on reflexive training.
If the malfunction is something more serious -- like a failure-to-extract, or as you called it a "double feed," -- then you will know quickly and can move to a secondary corrective action as we've already covered. If it's a broken part or other serious gun failure, you'll need a change of tactics. Again, clicking away at a "second-strike" trigger mechanism does nothing for any of these.
Also, from what I can tell most people pull the trigger, or at least attempt to, multiple times before realizing there is a problem.
This is a failure of training and experience. It is simply an incorrect habit allowed to develop. It should be weeded out just like jerking the trigger or anticipating recoil.
Hence my argument is that second strike capability, while not crucial, is good to have.
So, as you've conceded that you understand why TRB is generally the most appropriate response, and we've covered why looking at the gun is an unwise use of precious fractions of a second, so you're left defending the second-strike as a wing-and-a-prayer hope for folks with poor habits and training.
-Sam