Scour the web (including this site) for any before-and-after photos where tree removal really improved sight lines on various holes, etc. Maybe a little photoshop (fake tree removal) on your course would help, but would require more work, of course.
I have seen some great before-and-after photos and they show real, obvious, improvement. Once you cover all the valid reasons for doing so, a photo is worth a thousand words. Show some really great "after" photos, and then simply say--judge for yourself whether tree removal is beneficial.