The most common self-defense usage is quite close up - it's mugger be gone or some BG close in your house.
I have somewhere a study that shows the unskilled are reasonably accurate close up but when the distance gets longer, beyond 15 feet or so, the unskilled drammatically deteriorate in effectiveness.
Similarly, Karl Rehn did a test of skilled and unskilled with pocket guns and found the former had about a 40% useful hit rate as compared to the skilled.
The mall rampage, school shooting - is a high stress and perhaps longer distance scenario. Thus, it is at the extreme end of the intensity distribution. The modal or average civilan gun fight doesn't speak to the extremes.
This isn't even mentioning the needed automaticity for clearing, reloading, drawing, getting a good sight picture, etc. that might be needed for a stress filled longer distance shot.
We have a natural aversion to killing an innocent even for the greater good. Thus, if you contemplate intervention or SD in a crowded venue - I will opine that you have a moral obligation to obtain reasonable skills. Blaze away in your own home given that penetration is controlled. In public - that's a different moral circumstance.