Mike,

The 12th green is 2900 ft2. It is nine paces deep in it's narrowest spot, and 13 paces at it's deepest. It is a perfect strategic hole. Most tour pro's play the percentages, and other holes leave better birdie opportunities than #12. A tour player is better off to aim for the middle, or left under Master's pressure, and protect par because holes like 13, 15, and 16 yield a better chance for birdie typically.

Mike,

They're PGA Tour Pros, the best golfers in the world.
It's 159 yards at its longest.
They're normally hitting 7, 8 and 9 irons.  Even wedges.

The hole is almost perfect the way it is.

Why should they have a right of entitlement to make a good score ?

Why shouldn't the hole test them ?

Patrick and those who have played the hole,
   
Is the wind really so hard to judge on that hole?

I can see how it can be.
The hole is nestled back into the base of a hillside with tall trees.
It can be difficult to gage because the wind in the open areas where the tees are can be different from the wind at the green, and the hillside and trees on it can block or act as a backstop to the wind.

What also makes judging the hole more difficult is the shadows.

# 12 is probably the flattest green on the golf course so you get no assistance from the contouring with respect to depth perception, plus, since it's usually played late in the round, the shadows act like camoflage gear.

I am always surprised at how often the pros hit the ball in the water there.

I think there are a couple of factors that lead to that.
While you know the water is there, in front of the green, going long seems like it could extract a far more severe penalty.

That hillside is awfully close to the green, as are the shrubs and back bunkers.

If you go into any of them, the shot back to the green is frightening, and, if you go in the water, you have to replay the shot from where you were, or, go to the tee side of the water and take a drop, where you're now faced with another intimidating shot.

So, it's not as if the water is the only thing you have to be concerned with.

What you can't see from the aerials is the dip in the terrain behind the green, especially on the left side.

What I am surprised by is that more players don't go at the right side, especially when the hole is there because the margins for error are so much more substantial.

Look at the aerial Mike posted.
Look at all the room right and long right.

The putt from the left side of the green to the right side of the green is supposed to be the slowest putt on the golf course, so, I would imagine that the approach from the right or long right would be rather quick, but, it just seems like a natural bail out zone.

While the carry is slightly longer, it's not substantively longer, and, these guys are PGA Tour Pros, the best golfers in the world.

So, I remain mystified by the play on # 12.

Especially given their superior distance control and spin they put on the ball.

I'm not so sure that spin or excessive spin is an asset on this hole.

These guys are hitting lofted clubs, HIGH, to a relatively flat green.  There shouldn't be much need to spin the ball, especially when spin may take the ball to a watery grave.

I also read or heard somewhere this week that 12 green picks up speed on the right half towards 13 tee. So wouldn't it make sense for mortal golfers to take an extra club and miss long right (right of the bunkers) which would leave a pretty ordinary chip instead of bringing the bunkers in play by going for the middle of the green?

I think that's a reasonable strategy.
Perhaps the fear is an overcooked fade or a ball that gets away from you, or a good gust of wind.

Perhaps pressure and the knowledge of what lies short, long and left are the culprits.

Patrick,
   
I'm not thinking about spin in terms of backing the ball up, but in just getting it to sit when it lands. The low trajectory, low-spin shot I usually hit would dictate that I play the hole long right. No way I want to be over the green in the rear bunker.

A low trajectory shot is at a distinct disadvantage when playing the hole.  A low trajectory shot would make the hole exponentially more difficult.
 
How many times have you played the hole, and what is your success rate for getting on that green ?

I've played it a half a dozen times and never missed the green.

However, I have a bit of an advantage.
The 13th hole at Pine Tree is a mirror image of # 12 at ANGC, except that the 13th green at Pine Tree may be narrower, more angled, and prone to more wind at higher velocities.
And, I've played that green a 100 or more times, so, for me, it's a very familiar, a very comfortable feel.

I know I've probably just jinxed myself, but, my scoring average on the hole is below par.

One of the things that fooled me about ANGC, from a TV to a playing perspective is that some of the holes that I thought would be easy, were harder than they looked, and some of the holes I thought would be hard, were easier than they looked, and, some of the holes were true to their TV form.

I just don't understand why Nicklaus always wanted to take it over the front bunker when the pin was right. That is the smallest possible target isn't it ?

I think that's a good strategy for Nicklaus.
Remember, he hit a high fade and a high fade, aimed at that bunker, should get good results.

Look at the aerial Mike posted, the position of that bunker in relation to the tee and the flight of a high fade over that bunker.
I definitely wouldn't attempt to hit a draw to the right side hole location.  A high fade seems logical.  And, if the ball doesn't fade, you're not left with a bad recovery, even if you go in the front bunker.