Power
The work of a caddie isn't exactly glamorous, but just because they fetch balls and bags for a living doesn't mean they don't affect things. If you're the caddie, you're not the one who's a famous golfer, but you're his or her only confidant during some of the most crucial moments on the links. That's not to say they'll definitely ask for your advice, but when they do, you've suddenly become a critical part of the process.
Of course, all of this assumes that you're working for a pro. The vast majority of caddies are just part-time bag haulers, and almost no one's going to them for advice. And if some businessman on a lunch break ever did, who would care? Those caddies have about as much power over the round of golf as a dog does over a game of fetch.