Paul:
When we are building a new course and are going to build USGA greens, we shape the well and subgrade rather than at the finish grade level, to save a step in the process. The advantage of this is that once I approve the subgrade, then I know we can keep those contours at the surface just by probing through the sand. If we shaped the finish grade, and then had someone core it out as shown in the picture, I'd have to trust that they get everything excavated just right ... and I've seen too many operations such as pictured above to want to do that!
On existing courses where we are rebuilding greens, finding a contractor who can core things out just so is crucial to the process. The best job I've seen was by a contractor whose first step was to have a crew excavate a two-foot ring around the green by hand, with flat shovels ... the workmanship was better than anything I've seen, and it enabled the excavator operator to start coring out the rest from just the right elevation. I've never seen anyone else do as good of a job.