You ever notice when driving a car, that if you turn your head sharply to one side, your car begins to drift that direction? That is how famous author, Stephen King, got run over and nearly killed - a driver was distracted by his dog in the back of his van, turned around to deal with the dog, and drifted off the road into King. The moral of the story - your body (and your car) goes where your head (or your vision) goes.
In a conflict, it is often best to face the apparent danger and get your hands into the center of the conflict. From this position, your hands tend to get in the way of incoming attacks. Plus, the distance from the center of the conflict to where you have to put your hands to make a technique is usually very minimal.
But how do you figure out what is the center of the conflict? The only way is to point your vision directly at (or through) your opponent's centerline. Then your line of vision defines the center of the conflict. Then just put your hands on that centerline.
Try this in randori for a while... Put your vision and your hands in the center of the relationship. Then try looking away and/or moving your hands away from the center and judge how difficult the opponent is to deal with. I think you'll find that keeping your vision and your hands in the center of the relationship pretty much universally improves your performance.
In my class, we tend to call this the "cowcatcher" principle. Check out this interesting video of another interpretation of the same idea - just implemented a little differently.