Wasn't it Tiger Woods who started the tradition of removing his cap to shake hands at the end of the round? I don't remember it being such a show until Tiger started winning -- of course, in those days, Tiger was winning so often that everything seemed attributable to him.
I agree that it's become a bit of overkill while you wait for the 15-handicaps in front of you on the 18th.
For me, traditions are only important to the extent that they further perpetuate the game: being responsible for one's own score, fixing your ball marks and divots, going to the 19th hole to relive the round, etc. From that perspective, father-and-son/daughter golf and caddie programs that engage youngsters are probably the most important traditions.
I also think it's wonderful for a golf club to have one competition a year where outsiders can participate and everything is done to give the event a character of its own. There are so many examples in Britain: the President's Putter, the Worplesdon Foursomes, the Sunningdale Foursomes, the Halford Hewitt, the Carnegie Shield, etc.
One tradition I enjoyed in Scotland was signing the Visitors' Book ... at Dornoch I signed the same book that Pete Dye and Herb Wind had signed 40 years before me.