How about allowing wedge shots from the greens without the shot totally crapping out.
There are times when you are on a very long green or when there is a protrusion between your ball on the green and the hole where you cannot putt. You need to be able to use a wedge. I have seen Pro players do it, so why not allow it here?
Also, PLEASE have some indication (more than the little graphic) that you are on the green or fringe. It is sometimes impossible to tell the difference and it makes a lot of difference in the stroke.