Here is what Flynn said about trees:
'The pleasantest type of course is one where the holes are segregated, that is where the hole you happen to be playing is well apart from the others. In order to have this kind of course it is necessary to secure property that is already wooded or to do considerable planting of trees.' (Italics are Linc’s.)
' The old idea was to have golf courses as free from trees as possible. This notion, no doubt, was imported from Scotland because when golf was first taken up in the United States we knew very little about the game and modeled our courses on those of the Scots which were, for the most part, built along the seashore where there were no trees.
'It is impossible to conceive that the 'Canny Scots' would have denuded their courses of trees if there had been any there originally. As a race they are entirely too thrifty for any such waste as that.
'Today the old ideas have been discarded and the prevailing belief is that trees, most emphatically, have a fixed place on a golf course. This is true for many reasons:
First—Because there are few, if any, sites available that are devoid of trees and it is a costly operation to cut them down and remove them.
Second—Trees add beauty to a course forming picturesque backgrounds and delightful vistas.
Third—Their shade is most refreshing on a hot summer day.
Fourth—They are of great practical value in segregating various holes.'
'It might also be that moving a tee slightly to the right or left precludes the necessity of taking out some beautiful tree. This also applies to green sites. Sometimes a slight change in the alignment of the hole permits the architect to keep a specimen tree or trees which may also act as a key turning point in the hole.'
Source: Flynn articles in USGA Green Section Record, 1927.
I think the fuller version of this article says more about the PLACEMENT of those trees. This is taken from the Linc Roden Feature Interview.
I think my home course, Rolling Green , is an interesting case in point.
There were trees that Flynn designed around . Most seemed to be for turning points.
There were trees added well out of play in the 30's which seem to meet the above standards.
After 35-40 years the evergreens arrived to fill in open spaces , deal with safety issues, and close off angles of play to "make the hole harder".
To say "trees belong on golf courses" needs to be fleshed out. "Where" is the question.