In many sports you are required to make rapid mental calculations to estimate where the ball is going to land as it spins its way towards you. If you can meet it at just the right moment you can send it off to a new place and increase your chances of winning.
All of this happens at speed and it takes enormous skill to keep your eye on the ball at the moment of impact. Also, in a game like football or hockey, you need to determine where all your team members and opponents are likely to be.
With golf you have plenty of time to prepare yourself for the stroke, and hopefully nobody to interfere or distract you. But the ball is tiny and the place where you need it to land may be equally tiny - essential therefore to keep your eye on the ball when you strike it.
Why do golfers sometimes struggle? The reason could be practical, emotional or physiological. That compulsion to look away in the direction you want the ball to go could be due to nerves, or habit, or technique.
Alexander lessons can often help as they focus on the skills of Direction and Inhibition. I couldn't say they would make you into a better player but they would probably help you to play at your best:)