Tim,
I recall, as a 12 year old interested in golf architecture, reading many of the articles the NGF and others put out, including the then new World Atlas of Golf. It seemed, in theory (1960's style) that there should be a designed relationship between approach shot and contours.
The general idea was along the "long shot, big green" proportional design. "long shot, easier putt" was espoused as being more fair. My mentors always made the front of the greens concave, to help shots that hit the green, hold the green. If a long hole had a narrow green (for whatever reason) they tended to make the green more steeply concave, with up to 3% inward slopes.
Someone wrote that they assigned a difficulty value to each shot on a hole, from 1-3 (easiest to hardest). They felt a par 4 would be too hard if it was 3-3-3=9, or too easy if 1-1-1=3, and strive for somewhere around 6 on most holes. While a formula, it makes some sense. If you manage a successful tee shot on a hard hole, and the reward is an equally hard approach, which yields a hard two put, where is the strategic reward?
Way back in time, George Thomas had some thoughts, too. He felt short hole greens ought to be steeper front to back, to help golfers "check" their short irons, while long holes ought to be flatter back to front since he anticipated a roll on shot. For a long time, I felt this should be reversed in modern golf, with longer shots having steeper back to front slope to hold long irons, and flatter ones for short irons (more natural spin, less ball mark damage), and sometimes designed the back to front slope at about 10% of shot length, i.e., 1.5% for 150 yard shot, etc.) However, greens got too steep for longer shots. Whenever I researched it, I found 1.33% was all needed to hole average players shots, no matter what the length, and another architect pointed out to me that average players prefer the flatter slopes to help their ball roll all the way to back pins, rather than "kill" near the green front. So, back to front stays within a pretty narrow range for me, influenced more by green site slope, visibility, etc.
My mentors also taught me the "coin throw" but used it more for landscape plantings or mound placements.
Most of the tour pros I have worked with, or spoken to, prefer the green middle to be mostly the flattish surface that is the safe shot. They also dislike knobs in the middle, because changes of grade midway to the cup are the hardest to read. They also like to position tee shots to be aiming right into an upslope, and want about 10% or approach length in depth and width. They will use back slopes to bring balls back closer to pins, and consider any rolling side edges as bigger strategy deterrents than hazards (which they don't think they can hit). So, if anything, the random hills and valleys would be further apart on long approach shot greens, and perhaps closer (by a bit) on shorter holes, or back to the old "long approach, easier putting and/or larger target" at least to some degree.
Overall, while I understand the random beauty of the coin toss design method, somewhere, deep down, I have to believe that a conscious placement of green contours fits the game of golf better than a haphazard one. Or, at least, I think players do.
As Forrest Gump might say, that's all I have to say about that......
