When to adjust the sights.....
When point-of-aim and point-of-impact are different.
True, mostly. For a duty/off duty/defensive handgun I too adjust to intended point of impact. I prefer 25 yards for this setting, since I think it is a good balance distance between very close in and distance shooting out to 50 yards. That said, I am not overly picky about it, as long as I have correct horizontal sight alignment. My EDC semi-auto pistols (S&W 6906 and Glock 26) are not elevation adjustable, and I have never missed it.
But 'mostly' is not always. In PPC competition most shooters want to hold at the neck (base of head) at 50 yards as it is easiest to discern and hold most precisely at that distance. The stock sights on a revolver will not allow this. so gunsmiths building up PPC revolvers add a sight rib which can be adjusted so this neck hold places the rounds in the x ring at 50 yards.
The early BoMar ribs have large and obvious enough screw heads to allow a quick rear sight adjustment on the line, so we always carried a screwdriver for this purpose. Later ribs, such as the Aristocrat, allowed the front sight to be moved via a sliding button to a pre-setting for 7, 15, 25 and 50 yards. Needless to say, these pre-set adjustable front sight ribs became predominant.
Early on with the L frames, S&W offered a version with a tall front sight designed to allow this neck hold at 50 yards in a leg match revolver. Since normal revolver sights did not allow this range, so this would be advantageous, or so I hoped. I got one of these models with that intent in mind. Unfortunately this coincided with so much more work in both my LE career (I was in admin by this time) and teaching career that something had to go, and it was PPC matches. I still have this revolver, with a lot of custom work in it, but unfortunately it never saw the heat of competition.
That exception aside, back to serious use. I have done a fair bit of instruction in defensive handgun use. One of the courses of fire I was mandated to do in the CA PC 832 class had a maximum distance of 15 yards, with a generous time allowance. It seemed too minimal, but given the time constraints of a one semester class combined with students who may have never picked up a handgun, and in retrospect it was a decent starting point to get shooters to before they later applied to LE and were sent to the basic academy.
One of my objectives was to show how well placed shots could be with no reliance on the rear sight, thus no adjustability. I had everyone (including me since I was demonstrating) cover their rear sight with tape. I wanted to demonstrate, and have my students experience, the effectiveness and efficiency of a flash front sight picture. One of the points I made was that the closer one was to their assailant(s), the more quickly they had to fire effectively. The students very quickly picked up on this, since all they had to do was concentrate on the front sight. Those who had some prior experience shooting were surprised to see how well they did with just the front sight. No one used the front sight until we went from 10 yards to 15 yards. By this time the habit was ingrained; the front sight was key to shooting accuracy.
The following semester we went into night shooting. Concentration on the front sight and acquiring a flash front sight picture became even more critical in low light.
So, in any discussion and analysis of sight adjustment/sight alignment, I submit the most critical element, if far enough distant to necessitate sight use, is concentration on the front sight, getting it set on center mass, then squeezing off the rounds