I have always thought that the hole is 4.25" because that size hole just will allow a ball to go in the hole with the flag stick in the cup. If the hole was 6" that would increase the gap between the flag stick and the edge of the hole from 1.875" (based on a 1/2" dia. flag stick) to 2.75" That is a huge increase, and I feel it would affect just as many (or more) shots from off the the green than it will putts. The number of hole-in-one's, hole out from fairway, green side bunkers, chip in, would all increase drastically. And this would increase the luck factor instead of decrease it as the OP has suggested.