I was hoping to hear from the man who designed it, and see his explanation for why that didn't happen.
John:
I was hoping you would buy my book about the routing of all my courses, including Streamsong, when it's available, and then you'd have a definitive answer.
In the meantime, I'll just say that neither Bill Coore nor I ever considered a hole where you are suggesting. The line of sight is no good, and there's not much room down by that forward tee for off-line shots.
At one point, Bill and I did look at a very short par-3 from high to high, over toward the green of #15 Red. But I didn't like the flow of that coming so soon after the short 5th, and I was worried about intruding on Bill's 15th hole with our little one. If you look at Google Earth, you'll see that a bad pull toward the green you suggest could wind up pretty close to Bill's 15th green.
It was my associate Brian Schneider who suggested going across the water instead, and I liked the idea immediately, because it had the scale of the 9th hole at Yale, and because it highlighted the most dramatic features of the property. The suggestion appealed to our client, who had always liked the look of a green site across the water [from a different angle]; plus, the client had been worried about the short hole because of safety issues.*
It always puzzles me that so many people complain about what is the most photographed hole on the course, and the hole that is used for nearly all promotional stuff by the client. I am not the least bit sorry we built it.
* The banks going down toward that big pond were considered unstable for machinery, to the point that we had to have automatically inflated life vests on the bulldozers, and a spotter if we worked in that area. Their concerns about liability would have also extended to players on those slopes looking for balls, after they missed the green of a short hole high in the dunes.