If the trees on the right were cut down, the view would be directly into the neighboring Mountain View Cemetery. Cutting them down would also not only provide a questionable view, but would also increase the likelihood of sending a sliced Titleist into the middle of a funeral.
Needless to say, I'm for keeping those trees. They provide a needed boundary between the 12th hole and the cemetery without truly constraining the fairway (the presence of the cemetery is what constrains the hole, and the trees actually keep some balls in play that would otherwise be OB).
The trees on the left provide a bit of a buffer between this hole (the 11th) and the parallel 9th fairway and 14th tee.
The trees behind the green don't block much of a view, since the second shot is uphill with the rock quarry right behind the green.
This hole plays rather open, and as you can see the view from the tee is already pretty nice.
So I would not say this is a good example of covering up long views and interesting golf rolling terrain. There are some holes at Claremont where trees pinch things too much (it's probably unavoidable given how small the plot of land is). But this is not one of them.
If I could make one change to this hole, it would be widening the fairway on the right. That's the angle you want into this green. The land there slopes from right to left, so it would be a good challenging tee shot where you would want to hit a fade to try to keep the ball from rolling back to the center of the fairway.
The greensite is where the REAL interesting golf terrain on this hole is. The green is set in a mini-quarry. You don't have to miss the green by too much to have your ball careening off of the rocks.