"there is no realistic run-up option into #1, 4, 11 and 13? ...these holes require purely aerial approaches....in theory you can run it into 1, 4, and 11. In theory. But in reality, those aren't realistic options"
Shivas,
With all due respect to you, I think you are mistaken. The 1st, 4th, and 11th actually are often very difficult to hold from the air in common winds.
1st : if you are attempting to reach in 2, with let's say a 4-iron, you might find that it's best to hit ground a few yards short of the green. Perhaps not quite a run-up, but not aerial either. If it's your third from short yardage, a putt or run-up is to me a far better choice than landing on the green.
4th: Whether into a wind or downwind, a low bouncer is always a good option. And if it's your 3rd from the right, then like with Ballybunion #6 and Dornoch #6, a putt will win closest to the pin.
11th: From medium range, c150 yards, a high shot might seem to be the best, but not only choice. From short range, as John Foley says, "You can definetly hit a run up on #11 from the right side. It just will not be your second shot!" But John is slightly wrong. I have more than several times seen a 2nd shot from very close. Perhaps John meant it just won't be YOUR second shot.
13th: Even the 13th, if heavily downwind, might best be played by landing just short with a bounce. A shot that hits the green very often goes over the back.
Run-up shots on hilly courses often require a medium trajectory with just one or two bounces, and very often the shape of the shot will tell it's fate. Tommy N. recently saw, and commented on, Winged Foot East #17 as a classic run-up shot, and he's right. A very good option there is a low draw to a doubly-canted fairway (on a par-3 !) that first feeds the ball left towards the green, then turns it back right and up onto the putting surface. A fade won't work, nor will a medium-high draw that carries too far.
Sand Hills abounds with such shots.
neil