The point of the better action shooting games is to introduce stress into the accuracy equation, mimicking in a small way the stress of a self-defense situation.
Shooting accurately and quickly under stress is obviously a much different thing than carefully squeezing off shots at paper targets.
One exercise the wife & I had during an introductory tactical training class was used to illustrate that.
After target shooting exercises, we then each had to draw, put 5 rounds into a torso target. Score was based on a combination of time and accuracy. Less accuracy added to the time. Best time wins of course.
Once people felt the pressure of having to get off 5 shots as fast as possible, accuracy went down dramatically. We each did it multiple times. I got the best time/score because after one horrible round, I settled down and concentrated on making it 70% accuracy / 30% speed rather than the other way around. A smooth draw is better than a fast draw.
Their point was an extra second that gets double the center mass hits is going to be the life saver. But it also brought home how even a little stress can have a significant effect on accuracy.