Seems to me that it's a no-brainer that the course and super should have a tree management program that, among other things, gets rid of trees that for reason of age or disease or whatever pose a danger. At my club we recently took down what seemed to me to be pleasing tree, very large, that posed no danger. Yet our powers that be were on top of it, determined that the tree was so old that it now posed a risk, and took it down. I kind of miss the look of tree, which did not impact play significantly, but the correct action was taken. Trust the experts.