I think they're o.k., if worked in as part of a "natural" landscape plan that is suitable to the geographical location of the course and are native to the area. For example, if the course has been built on a ground that once was woodlands that included dogwoods and serviceberry trees, then placing a few of these trees here and there as a remnant of the woodland, in a way that looked natural rather than formal, and did not come into play, would be fine with me. Personally, I planted several serviceberry trees at the side of my house that borders a national forest. They're in the forest, so bringing a couple into the yard works for me. It would be the same for me on a golf course. I'd say the same for perenial wildflowers, such as goldenrod, black-eyed susans and cone flowers, popping up here and there in a "natural" area on a course.
Also, I agree that "safety" is not a good excuse to have trees. They may provide a false sense of security, among other things, while at the same time not being reasonably effective. My club is also an old club on a small piece of property. Several years ago we took out many, many trees, of which many had been originally planted for "safety" reasons. The tree removal has not, in my view, created a safety issue. By the way, at an event at our course in the past week a PGA rules official told me that he had never been to our course before, and wondered whether we had lots of golfers being hit by errant shots because everything was so close together. I told him it was not a problem. I think the problem, and the tree line solution, is more imagined than real.
P.S. My understanding is that the name "serviceberry" (a/k/a "sarvisberry" in the mountains of West Virginia) derives from the fact that they are very early bloomers, the first out in the mountains in the spring, and the flowers were therefore used to decorate for church services, when the circuit riding preacher first came through in the spring to take care of deaths, births and marriages that had happended over the winter when he could not get over the mountains and into the hollows. True or not, that was the tale I was told many years ago as a child in West Virginia.