Ah, Sam - you have started a thread that involves my biggest pet peeve in golf architecture. I call them Stupid Trees and I will get to them in a moment.
First, although Tom Doak (and others) know far more than I about the effect of trees on light and air circulation, for this reason alone I could live without them. That is probably too severe, but since I can't tell a "good tree" from a "bad tree" in this regard, when in doubt, cut it down.
Now, about Stupid Trees. I have no problem ARCHITECTURALLY with any tree that is an impediment to your shot either from the rough or more than 150 yards from the tee box on a par 4 or par 5. You hit it in a bad place and there's a tree in your way, you get what you deserve. Also, I have no problem with a tree impacting the optimum shape of a tee shot so long as the first 150+ yards are not subject to tree problems.
What I really, really do NOT like are what I (and others) call "bunkers in the sky" - trees that are an impediment to a straight line for the next shot IF YOU ARE IN THE FAIRWAY. Philosophically, I believe that if you hit a shot to an "approved" place, then the degree of difficulty for your next effort should be a function of the golf architecture ON THE GROUND. After all, any Greens Committee Chairman can plant a big tree. It takes skill to create shotmaking challenges by building them on the ground.
Stupid Trees come from two sources. The most egregious are those that are planted on purpose and the 18th hole at Pebble Beach is the poster child for this heinous offense.
However, most Stupid Trees start life as little saplings that line the fairway and 20+ years later, they overhang whatever side of the fairway they have now grown to obstruct. This is why most tree removal projects are very, very, good.
I have posted longer harangues on this subject on other threads and I just couldn't resist another cathartic opportunity.