TEP, as usual, you raise some good issues. In fact, in the 1950s at Pinehurst, they piled sand on top of the place, and it managed to build up something of a crown - gradually.
You are right, that sand splashed from bunkers won't get to the middle of greens, but it does raise a kind of wedge between that bunker and, say, 10-15 into the green. That's the kind of build-up, by the way, that led to signifianrt changes in Riviera's contours, enough so that when Crenshaw & Coore "restored" them in the mid-1990s they opted to leave about half of the accumlated elevation that had built up rather than go bakl radically to the lower, original contours built by Thomas & Bell.