What if the hole isn't great in the middle of the green, but it is when cut on a finger, or an eyelash, or an elbow? This seems to me to be a most irrelevant point in the ultimate judgment of a golfing hole (from tee to green.)
Let's see if I can explain myself. A great putting surface might provide multiple opportunities to hit different types of shots (runner, bounce and release, high spinner) to different pin locations, yet the shot to the middle of the surface might not be as challenging/worthwhile as the others.
Certainly, access FROM the center of the green to all hole locations (with the exception, of course, being #6 at Riviera, where a sandbox obscures this play) should be a principle of great golf holes. Use the tucked/hidden positions to trick the brash/bold/stupid golfer, yet allow those tucked and hidden positions to be accessible (30 feet at most) from the geographic center of the putting surface.
I'm all for sectioning of greens, as long as access to them is provided (and not just for the high, faded 2 iron with blistered feet.)