I am 6'3" and I have been trying to figure out this question for more than 50 years. Here are my conclusions...
The major advantage of being tall allows the golfer to create a larger arc in their swing, thus, generating more clubhead speed and, theoretically, longer distances and more height to their shots for softer approaches.
But, I also know that the shorter golfer has shorter arms which can move more quickly through the hitting zone, thus creating addtional clubhead speed which, in turn, nullifies the advantage of being tall. So, being tall does NOT necessarily mean longer distances. (Jamie Sadlowski, long drive champion, is 5'11" and has a clubhead speed of over 145 mph.)
Where I think the real advantage lies is being short. Think about going up in an airplane. The higher you go, the smaller things on the ground appear.
The same is true for golfers. Tall golfers' eyes are farther from the ground, and consequently, farther from the ball. This would lead to the conclusion that the ball would seems smaller to the tall golfer. If a study were done of who strikes the ball more solidly on the clubface, I would venture to say that shorter golfers might be the winner because they perceive the ball to be a larger target than the tall golfer. Those of us who golf with any regularity understand that more bad shots are created by off-center hits on the golf club. Thus, the advantage goes to the shorter golfer, since they are seeing a larger ball to hit.
In addition, since almost half of the shots in any round are taken on the green, I think the same can be said for putting. The shorter putter sees a larger ball, a larger cup and their eyes are closer to the line of the putt.
In conclusion, let's look at 11 of the all-time great golfers and their height...
Gary Player - 5' 6"
Lee Trevino - 5' 7"
Bobby Jones - 5' 8"
Tom Watson - 5' 9"
Ben Hogan - 5' 9"
Jack Nicklaus - 5' 10"
Arnold Palmer - 5' 10"
Sam Snead - 5' 11"
Tiger Woods - 6' 1"
Phil Mickelson - 6' 3"
I don't think there is an advantage to being tall nor short, also the list you gave reinforces what I just said. The height of the best golfers varies all over the map.
Average height of the PGA pro is around 5'11", but the deviation could vary +/-6 inches.