That is a bad analogy because darts is a one motion game while pool is a 2+ motion game. A better analogy would be putting, in golf, because you have something hitting a ball that hits a target. Rarely would a golfer look at the target (the hole) rather than the ball. In pool it is even more complicated than that, because you have something (cue) hitting something else (cue ball), which hits something else (object ball) and goes into the target. And in 3C forget it, there are targets all over the place in the course of a single shot.
The other problem with your dart analogy is that almost every precision sport tells you to keep your head still. You would have a hard time even hitting the dartboard if your head was moving enough to focus on the dart. The implication of the still head is that you cannot have your focus be something that causes you to move your head - which explains why you do not look at the dart.
