The kidney-shaped green can be an effective way to dictate the line of play. IMO, it is best applied when the narrow portion of the green is in front with a single bunker or string of bunkers in the area where the green is absent.
Here my attempt at an illustration (G - green, B - bunker):
GGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGGGGGGGG
GGGGGGGGGGGGGGGGGGGG
BBBB GGGGGGGGGGGGGGGGGGGGGG
BBBBBBBB GGGGGGGGGGGGGGGGGGGG
BBBBBBBB GGGGGGGGGGGGGGGGG
BBBBBBBBBB GGGGGGGGGGGGGGG
BBBBBBBBBB GGGGGGGGGGGGGG
BBBBBBBBB GGGGGGGGGGGGG
BBBBBBBBBB GGGGGGGGGGGG
BBBBBB GGGGGGGGGGGG
BBBB GGGGGGGGG
Of course, the picture could be reversed along a vertical line through the center.
Suppose the green is used at the end of a short par 4 or long par 5, so the approach is played with a short iron or a pitch to a small green. Referring to the above drawing, if the pin is front right, the player can approach from the right and test his accuracy or approach from the extreme left and test his distance control. If the player doesn't hit to his favored side of the fairway, there is still a chance for a GIR, but leaves the player uncomfortable with the shot.
If the pin is back left, the right-side approach is desireable if the player wishes to take the greenside bunker out of play. A back right pin is the easiest for member play. If the hole is well-designed, the more desireable side of the fairway will have some risk (i.e. bunker placement).
Quite frankly, I don't think this type of green is used enough. Interested to hear other's comments, examples, and viewpoints.
Pete