Niall - I am not sure I see things as black and white as that. There is no doubt that trees too close to greens can cause turf problems, they can around tees as well however you need trees to be intimate in some situations, so its not a blanket rule and sometimes there needs to be compromise in the positioning. Some golf courses WOULD NOT benifit from tree removal. Some good golf courses are good because of the trees, a lot of the golfers like trees, it is the major opinion so I dont really think you will get the backing from the major bodies. That aside, there are areas on most 'treed' courses that will benifit from the chop.
We have argued with authorities that when we build new golf courses we will plant 15,000 trees which will benifit ecology and the immense benifits to birds, bees, animals, air......How do we now say "actually we want to chop them down".
I think the right trees need to be planted in the right situations, I have never bothered with tree grants because the authorities control too much the specie, you get the trees cheaper but you often get too many with too large leaves, you dont get much problem with a scotch pine or a silver birch, hawthorns and scrubbier stuff are ok, even oaks and beeches dont cause too much fuss.
Many clubs have had bad planting schemes, designed by a club member whose tree intrest has perhaps not understood things and the very worst has been the planting of clonic trees like the fast growing poplars and everygreens that grow 3 feet per year, if they are treated as nurse crops with a decent oak or something behind and then removed when the main tree is 15 feet then it would all be fine.