Geofff - alright, I'll drop the 'from a lefty's perspective' and put on my engineer's hat to deal with this one...
I think that the trees by the 9th green were removed for the sole purpose of construction, not for shot values. I may be way off base here, and feel free to tell me if I am. But that is obviously a man made dam on 9. Not sure if it was built at the same time at the course or not, but it looks pretty new in your photo. The natural topography shows that the green was cut into the hillside, thus the need to re-ade back to existing contours on the right side, hence the tree removal there.
So my case is that those areas, while they are devoid of trees in your pic, may not have ever been meant to stay that way. As an engineer I face the fact every day that while we want to impact as little land as possible, clearing limits need to far exceed the actual limits of the completed project, just so equipment can manuver, and so grading can effective and stable.
The way Yale was laid out, it certainly seems like each hole was meant to have it's own corridor,and that only certain spots - like 1&2, and 7&8 were really designed to be vast open spaces.
The site is so wooded, and the holes are routed so far apart in most spots, I dont think it was ever meant to have a Shinnecock or NGLA feel to it.