It seems to me from my reading of the site and the helpful posting of lots of historical aerials that the majority of what we here would decry as "over-treeing" has occurred, especially on Golden Era golf courses, because of the planting of trees long after the architect has left. Nevertheless, it also seems that the vast majority of these sites had trees when the architect designed them. These trees were at least tolerated, if not explicitly placed, by the architect, which makes them strategically significant.
Most aerials of courses I've seen early on were quite barren.
I am trying to wrap my head around how architects think about trees on their designs. Trees are a variable of GCA that the architect can be absolutely sure will change with time. Maybe some architects here can chime in with how they thought about the future of the trees on the courses they have designed? Did they make explicit plans for what might happen with tree growth in the following decades?
Often clubs simply ignore the "plans" for trees or suggestions by architects if they've made them. The committee sees an open space, and WHAMO! The next thing you know is there are trees filling the void. Some cultures are in love with trees, and don't understand their negative impact. In other instances committees seek to "beautify" their course and associate that with planting trees... which is easy to do.
What most fail to realize is those glorified sticks they planted with a few guys wielding shovels turn into water sucking, debris dropping, strategy killing behemoths. They grow slowly, so it's a bit like putting a frog in cool water and turning up the heat to a boil. By the time the club realizes the problem... it's huge.
Trying to cut a mature tree is tough, especially if it's graced with a cemetery-like memorial.
If I may play Devil's Advocate, imagine a fairly old course that had some trees on it originally and has not had any new trees added. Imagine that we now look at the course and say "it feels claustrophobic" and "playing corridors have been unnecessarily narrowed." In the absence of direct evidence from the original architect, who is to say he did not intend or plan for that tree growth? When we decry changes to greens, fairways, or bunkers, we have evidence of the architect's original intent. When we decry tree encroachment, if the trees are original, it is not clear to me that we have that same evidence.
Let's say the architect wanted trees... he could not forecast the end result as he could standing over a greensite or bunker scheme in production. Like plans in general... he just may have guessed wrong. He may never have envisioned trees fed with water and fertilizer to encroach as they had... for the architect is human and is fallible.
The question is fairly simple. Do the trees in question add to the course, do they harm the agronomy, do they kill the design-intent, do they cut off wonderful views, do they make the course monotonous, are they necessary for protection or not? These and other similar questions need be made. In other cases like Oakmont and The National Golf Links of America... the answers are pretty simple. Pasatiempo may not have been a course intended to have so many trees, but from what I understand they are vital in places to keep golfers from wearing golf balls.
Sometimes trees, and groups of trees are just butt ugly and should go. Sometimes the architect may have had trees planted and expected them to be thinned out, but never were.
One thing is certain. The tree will die at some point, so if it's a negative, there's nothing wrong with bringing about it's demise sooner rather than later.