I hate to jump into this....but here I go, head first....
Let's say a course is tree lined. Under those trees is what height of cut? Fairway?...nooooo...it's rough, and we know what rough does, don't we? It stops a ball very shortly after it lands in it. Therefore, trees do have a significant impact on how far offline a ball can go, even if the ball never touches a tree.
Now, let's assume a course has some very tumbly land, for lack of a better description. Let's also assume at least one hole has been routed along a spine of land. The green would perhaps be pitched from back to front on the intended angle of approach. If the hole were naked to the world, so to speak, and the turf was not overly irrigated and cut at fairway height for a significant width, wouldn't that make the approach shot more difficult, relative to a shot from somewhere up on the spine the hole is routed along? Of course. But, you say, it isn't more difficult than a shot from under or behind a tree, or trees. But, it would force a chip-out for a high percentage of the golfers, regardless of which course it is. Now, if chipping out is regarded as more fun than hitting a doable shot from an awkward angle, then the whole tree argument hits a snafu.
I would recommend taking out enough trees to make the golf course fun and healthy.
Joe