If two of golf's greatest swingers were so convinced of the importance of the top hand in the golf swing--and many others besides--it seems to me that we should give it some attention. By coincidence, I read about Henry Cotton and his tire drill--where he had his students whacking a car tire, first with their left hand, then their right, and then both hands. The drill was key, in his mind, to strengthening golf muscles, learning to use the hands correctly, and learning to make a square strike.
The other day I took my tire to the range and had Steve whacking it prior to hitting balls. What was remarkable was that Steve at first could not make any decent kind of strike using only his left hand. In fact he actually missed the tire on one attempt. Before long, however, he was striking the tire solidly and square with his top hand.
Golf is a two-handed game. However, for right-handed players, we generally need to give the left hand some attention and some training. We don't generally have to worry about our right hand getting involved--other than worrying about it getting involved too soon. The Henry Cotton tire drill is a good way to train that left hand if you suspect yours might not be working as well as it should.