John,
I don't know if I'm qualified to evaluate the ground game, but I sure have had to deal with it over the last two and a half months. I think Tom hit the nail on the head when he mentioned the through the green area. The best example of this that I can think of were the two US Opens at Pinehurst. Specifically, the shaved off areas around the crowned putting greens. Now, when the players ball runs off and remains on this fine cut of grass, the golf course has given him options for the next shot. Sure, he can pop it up and on but there are severe consequences for a less than precise shot. The ball can also safely be putted or pitched low with a 5 or 6 iron. As Americans, we are comfortable with the wedge, and our best wedge will probably be better than our best off the green putt or run-up.
The biggest reason IMO that there is not much ground game in the US is that there is really no need for it. Seldom do I feel that I must get the ball on the ground quickly. Also, the consequence for failing on a short pitch is not much worse than a 20 ft putt. Now, large elevation changes (crowned greens) and possibly bunkers change the entire complexity of the shot. The consequence of failure may be that the ball rolls back down to your feet or a thin shot (easy to do on a tight lie) goes over the other side. The decent golfer IMO is not no longer stopped out at bogey. 7,8, and 9 have been brought in play. How many of you have been on a links course near a green in regulation and made double or worse? I'm living on what I think is the best par 3 in the world and see 7s and 8s every day.
I have been playing links golf every day on a course that has severe slopes around the greens. Some of the crowns are shaved and some are not (making a putt or run up extremely difficult if not impossible). In determining whether to go ground or aerial, I look what's between my ball and the hole and how much green there is to work with. Purists, for lack of a better term, will not care for my conclusions. Personally, I think it's just easier to hit the ball over the awkward swales and let it run out or check. Sometimes this is not possible and a putt or pitch is absolutely optimal.
Here is an example. For simplicity let's assume no wind and flat, extremely tight lies on hard pan and firm, fast greens. I think most of us are familiar with the 17th at The Old Course. Let's say the flag is cut 25 ft past the Road bunker and the players ball is 10 ft short of the bunker. Impossible shot. Either a miracle 60 deg or putt around the bunker. No real options. Now, let's say that the players ball and the flag are 20 ft right of their original position. Now, the player has many options. I may try to hit a spinning wedge that lands on the top of the plateau that checks and runs. But I can also putt it up the hill or pitch it to the base and run it up. It's an easier shot because past the bunker there is a slope that runs toward the road. Right and left of the bunker, this slope gradually becomes flat. The difference is options. We just don't have many of these options in the US. Personally, if I can take the slope out of play, I do. But, it is only a function of how much green there is after the trouble area. If there is little green, the wedge stays in the bag. If a lot, I pitch it. Why not? Americans are just more comfortable with the wedge.
Finally, if you miss a crowned green and go into a bunker, it may be a blessing. You now have absolutely nothing to think about regarding club and shot selection. The only problem is whether the lie and stance are OK (which a lot of the time they are not).
John, I talked to Bruce at Renaissance Cup about the left greenside bunker at #9. It has no lip and he said putting was an option he and Tom intended (same at #3).