We have established that the heathland/parkland distinction is irrelevant to trees on golf courses in America.
I try to study one classic American golf course architect as much as possible and he loved trees. When they needed to be kept on the course he designed with them in mind. They came into play usually as doglegs.
As for planting trees he suggested that they separate holes, provide a backdrop and shade on a hot day. Don’t recall him saying “f with your shot”.
The problem is that trees planted after his courses were designed in many cases are in the way of the intended design. As one approaches the green these additions even ruin the original design at the green.
Great design by this guy was for the wayward golfer who needed to recover not as much for those who hit it down the middle and on the green.
Many golfers have 25 years or more experience playing courses with too many trees in play. They accept the penalty and adapt their game. Many come to believe the trees are necessary.
For me these trees make courses homogeneous. The land gets covered up and approaches from distance to the green are limited.
If you have a crappy designer or a flat boring property I can sympathize with the desire for some obstructions like trees or bunkers.
But great designers love the land as the chief hazard which challenges all randomly rather than some assuredly.
The most common trajectory of dissatisfaction with tree removal is hate—acceptance—love.