We don't have pistols. However, I respectfully disagree with you on trigger control. If my soldiers are engaging a bad guy with a pistol at 5 feet, I would much prefer that they dump the entire fifteen round magazine into the bad guy as fast as possible.
I understand your point of accuracy, and I think that's all well and good. However, and I see this a lot in the military, getting all of your rounds into a 1 inch and a 3 inch circle is highly overrated in a close quarters fight, in my professional opinion. What I prefer to teach them is to put as many rounds into a 9" circle as fast as possible. A 9" circle pretty much encompasses the entire region of sternum. A round in this area is likely going to hit something that the bad guy needs to survive. 5, 10, or 15 rounds, even with our wimpy 9mm, should hit enough vital organs that even a Taliban hopped up on opium and adrenaline should be put down.
I'm not trying to debate the need for accuracy. It's very important to be accurate. However, none of us are trying out for a pistol competition. I think the "cool" factor of shooting extremely tight shot groups works against the infantry a lot of times. Soldiers work on making their shot groups tight, instead of squeezing off enough rounds to put the guy down. You can certainly train to be both fast and accurate. However, in a fight that is 50m or less, I will choose speed over accuracy. That's with rifles, not pistols, however. The four fundamentals are important, but my opinion is that in a close quarters fight, it's time to throw all that stuff out the window and simply concentrate on shooting the bad guy faster than he can shoot you.
This is just based on my experience in training and combat. I understand that others may hold different opinions.
Kent