Without trees I think the quality of the course would suffer greatly. Harbour Town is a course where there is very little gray area, especially off the tee. If you hit a good shot then you'll have a good look at the green. If you do not hit a good shot then you are left with a recovery attempt, or trying to work the ball around the trees and into those very small greens; not an easy task. I see Harbour Town as a course that lets the player produce good shots and bad shots, but with a very fine line separating the two, and with very few shots that are neither good nor bad. If you remove the trees then you would remove that element of the design, and the course would then be receptive to all sorts of less than stellar shots.
As Mike Hoak mentioned, if the player felt that he could spray the ball and survive, often without penalty, Harbour Town would be unable to defend itself, even from players of much less skill than the touring professional.