One thing that I think can sometimes get overlooked when it comes to trees is that sometimes trees can be just as beautiful and good looking to course as say, massive sand dunes or something. Trees can really make a course look good, but then again on some courses it can make it look bad. I think trees arent exactly favored among some courses where a tree or even a few would make a few holes look a ton better. For instance the tree in the middle of the fairway at Sahalee #18 makes the hole.
There are also courses that are overtreed, from what I have heard maybe PV and Augusta. While the trees might not make the course bad or anything they might somehow detract from the experience of playing somewhere. In a case like Augusta, from what I can see on TV, the trees are very beautiful and I could not picture the course without them. However, if trees detract from the way a course is meant to be played, then they should be removed.
A good example of good tree removal might be at Kitsap Country Club, just ask Michael Hayes
A course that might actually need trees, well, theres gotta be some. A nice course called Harbour Point about twenty minutes from where I live recently cut down a couple beautiful trees that IMO need to be grown back. Its cases like this where trees are a good thing.