You must not golf much. What you say about a common dispersion of shots or shot group as you put it is true. The reason playing a curve helps a player manage his miss is because it picks a side for that dispersion to be on. Choosing the curve, or just knowing the curve, allows the player to set the edge of the dispersion area. If there is trouble out right, pick a straight line just left of the trouble that you know your draw will move away from. If your miss is a str8 shot (common for good players) then you will be fine with your miss. Every other shot will curve away from trouble towards your intended target. Yes some will overshoot and some will not quite get there so you still have a dispersion of shots, but none of them, save for the dreaded double cross where the player puts the wrong spin on the ball, will be in trouble. Same goes for fades coming off trouble on the left side. As mentioned, Nicklaus played his game as if there was a wall up the left side of the course that he'd never cross, pretty much always hitting a fade and some straight balls, but never curves in the other direction. It is about controlling the nature of your miss.In golf and pool you don't hit the exact target every time - you hit within a typical "shot group" area surrounding it, larger or smaller depending on your precision That shot group (your precision) doesn't shrink because you add a curve (in golf) or some squirt (in pool) - it only shrinks as you gain skill. That's why I don't think the "pick a side" technique works in pool and likely not in golf (I know of enough examples of pool pros being wrong to not automatically trust golf pros' opinions either).
By contrast, a guy intending to hit a straight ball can get accidental curvature to the left or right and that curvature can be to varying degrees just like the guys playing one shape. He doesn't know which side he will miss on and therefore is forced to play very safe lines to try to avoid trouble.
Simple example with a pin tucked on the left side of the green (favors draws).
The rightee fader aims right at the pin knowing his miss is at the flag and his regular shot has a lot of green to land on.
The rightee draw player aims at the right of the green knowing his str8 miss is fine and his draw takes him towards the pin.
The str8 ball player has one play and that is to put the center of his regular dispersion area far enough right that the left edge stays on the green by the flag and doesn't go off leaving him short sided. Usually that will put him enough right, that many shots will miss the green right. More likely, he will overestimate how tight his dispersion pattern is, choose a more aggressive line, and end up short-sided with a miss left far more often than either the drawers or faders.
Like I said, knowing the curvature of your shot and playing for it to affect where your shot group will land relative to the flag and hazards is vitally important in golf and a very common component of course management.
Again, for pool, knowing for sure which side of the ball you will be striking on and adjusting for that type of spin, even if the amount can vary somewhat, will similarly simplify your adjustments for the shot, tho not nearly to the same degree and that is probably why some pros play this way, not all. ALL golf pros play their shape or a shape that suits the hole if they're comfortable with both. Mo Norman was the only one ever to effectively play a straight shot.