I wonder why Dye made the green open up from the right rather than the left. It appears that the approach from the right side is the easier shot. Maybe the length of the hole is sufficient that one chooses between yardage and angle.
Also - how much do the trees right of the tee come into play? Should they be cut down?
I don't think the trees right are very much in play at all. The photo from the tee above is from the tips, which are elevated and should only be played by people who want to play from 7400 yards. The ideal line from there is probably toward the far bunkers, as Charlie mentions, and a pushed shot hit toward the trees doesn't have to be hit very high to clear them.
From more forward tees, the angle opens up pretty considerably. I played one tee up from the back when I visited last May, and they weren't in play at all from there.
To your first point, and the question of why the green opens from the right, it's another example of my earlier suggestion that Pete Dye GC isn't a course that has a clearly spelled out "Position A" on most holes. The key consideration off the tee is the angle of the fairway and shortening the approach as much as possible without yanking one into the hazard. If you muster the nerves to hug the hazard off the tee, your approach may be 20 or 30 yards shorter than a drive of the same length that's pushed slightly. I think that's plenty of reward without also gaining a wide open green front.
Furthermore, while the green's opening is angled slightly to the right, it's still a pretty difficult target to approach from the right side. The trees on the outside of the hole encroach a bit from the right side, and the bunker on the far side of the fairway from the tee is pushed up a bit to obscure the view on the approach. There's a bit of a swale in the green opening that will trap a weakly struck approach, and a slight push on an approach from the right side of the fairway risks getting hung on the hillside right of the green. A pull, of course, risks going into the creek.
From the left, you have a clearer view of the target (again, we see a hole where setting up the ideal visual for your approach is as much a challenge as simply setting up the most receptive angle). You're able to hit your approach slightly away from the creek and that hillside right is effectively out of play unless you significantly overclub. If you bail out just a little, you end up fairly safe with a pitch coming down the length of the green. It's not an easy up and down, but the likelihood of pulling one into the creek or pushing one onto the hillside is less from the left side, and those are the real disaster misses on this hole.
Personally, I'd rather approach from the left but it's pretty tough to play courageously enough from the tee to set up that shot. I tend to think the angling of the green opening to the right is more to help the higher handicapper have a fighting chance. The green isn't easy to hit and there's trouble surrounding it for the strong player. For a weaker player, laying up just short and right of the green gives an ample landing area and a pitch that, while tough to get close, is quite receptive to a simple bump and run. For the weaker player getting a stroke, pulling off that difficult up-and-down will likely win the hole. Even a pitch and a two-putt can make things interesting on a hole as tough as this one.