Pat - I've often wondered the same thing. This is a very interesting debate. I've tend to look back down the fairway or to the tee when I'm finished playing hole. I do think it gives a different perspective and can lend strategic insight, particularly elevated greens as Doug states. For those who have played Bethage Black, the view from the green on 2, 4, 5, 15, and 17 are quite revealing. As someone who has played this course a lot, these views reveal angles that are not as apparent from the tee. It also gives a different feel for yardages.
I think it comes down to the fact that a golf hole is a sequence of more precise shots. Drive is to a fairway, if you're good to a section of fairway. Obviously, a strategic hole favors a section of fairway. An approach or tee shot on a par 3 is targeting for most of us a green, for the better player a section of green that is considerably smaller than the target area for a drive. A long putt is targeting the imaginery "3 foot circle," while the shorter putt, the hole, but no more than one foot around the hole. Then of course we have the tap in. When I stand next to the hole, look back to the tee (if I can see it), I certainly gain a new perspective on the angle of play. Instead of looking from the tee at a hole from broad areas to small ones, you are now looking at a hole from the smallest target back to the largest. I think it makes a difference.