Ian,
Like others, I like the conversation flip to get them thinking.
What can trees do architecturally? Strategic bunkers in the sky......force a fade or draw, (if desired, many don't care for this) ....... conceal the true direction/velocity of the wind.........safety......screen views you want screened.......frame nicer views from selected points (golf is strongly sequential, using them to frame views from the tee or green, where nearly everyone congregates is easier to do than in a village square or some such).....add seasonal color......or fragrance.......On the negative side, they can slow play (especially low branching evergreens causing ball searches, etc.)
What do you say when they reply "General beauty" or "Much needed shade?" Certainly sun issues are getting a lot of play these days, and I can see some lawyer suing a treeless course for removing trees and causing skin cancer....but of course, I am a bit cynical like that.....
In that WSJ article on trees, Keith Foster mentioned he thinks many clubs over do it. I suspect many old members recall the course as a cornfield, and don't want to go quite that far back in evolution reversal. His is probably the right compromise over the wholesale approach at Oakmont.