If the targeting is selectable, then it would stand to reason that Professor Crater in "The Man Trap" forced his phaser to deliberately miss Kirk and Spock when he opened fire...
Perhaps once the target has been acquired, it lights up or does something to display to the firer that it has a lock and all they do is fire?
Doesn't Crater use the older WNMHGB phaser? Perhaps that model lacked the self-selecting targeting feature of later models. I don't see anything which might be a screen on that prop...
Oh cool! I had forgotten about that. Thanks for the reminder.
I guess the lack of use could be explained by confidence in one's own abilities (and in one's abilities to predict what the automation will be doing, without having to confirm this beforehand from a screen). And that could apply both to aiming (and auto-aiming) and to mode selecting. Amusingly, when the function is seen used, it's by McCoy, our designated gun klutz (his phaser fails to fire in "Return of the Archons", is accidentally set on kill in ST2 when they board the Regula station, and may well have finished off "Nancy Crater" by accident when he probably would have preferred to stun the beast).
This is more or less exactly what I was thinking.
Perhaps the fact that the screen got so little use led to future Starfleet hand phaser designs lacking a targeting screen all together. The movie phasers and the TNG+ phasers all seem to be able to hit targets off bore-sight, and do so without any kind of visual sensor display. I suppose that the addition of an actual video screen sight was ultimately deemed frivolous and was eventually omitted.