Mike:
If you hadn't noticed, there are lots of clubs taking out trees for lots of reasons.
Two stories from my consulting days:
1. At SFGC, I mentioned years ago that the pines and cypress were all the same age, and they were all going to die around the same time, unless they started taking out one section at a time and replacing them [or not replacing them]. Nobody took it at all seriously until one Sunday morning when a huge pine fell straight across the first green!
2. At Medinah, when we were working on Course #1, I noticed that there would be a better view of the dome of the clubhouse if they took down some trees that had been planted in front of the clubhouse, near the pro shop. The committee members didn't like the idea; they started talking about maybe it would expose the a/c units on the roof. Then, when we got up there to look at the trees, someone mentioned that the year before, a member had been KILLED when a limb fell from one of the same trees! My horrified look got them to think about cutting down the trees.
The only place I have felt really endangered by the potential for falling limbs was at Royal Wellington GC in New Zealand. It's very windy and they had a lot of terrible trees around back in those days. I think they've thinned out a lot of the dangerous stuff now.