Noel:
Given the land that Tillie found at Alpine it's an amazing feat of engineering / design in the first place. The pitch on the property -- particularly as you make your way to the back nine via #10 is something to behold. I personally believe that if Tillie had the benefits of modern equipment a few things probably would have done that provides for a more seemless transition to that side.
I can remember playing the original 10th hole 25-30 years ago during high school matches at Alpine. That hole, and to a lesser extent the one that exists today, have to rate high on anyone's quirky list. Don't get me wrong -- I love the green but the demands are clearly beyond what one normally finds at any Tillie layout that I have ever experienced as one attempts to climb that hill (they should call the hole the Matterhorn!).
Clearly, Tillie adapted to the terrain he found. I've always believed the greens at Alpine are among the toughest you'll play particularly late in the season when they are really firm. You're right Noel -- you can putt off a few of them -- especially #10.
There is no room at Alpine for the ground game. The turf is usually watered beyond what is needed because too many members erroneously think the "green is golden" rule of thumb.
I've always believed that if Alpine was truly rock firm it would be an extremely testing course -- especially if the rough were cut back allowing poor tee play to be further penalized. The small tilted greens provide enough of a penalty as is.
Even at other Tillie layouts in the metro NY area there is way too water applied on a daily basis to pacify ignorant membership by keeping everything soooo green. Clearly, some of these courses would be just as good, if not better, if firm conditions became the dominant pattern. The result would be enhanced shotmaking skills needed to overcome the qualities imbued by its creator.