When thinking about golf and style the ubiquitous hat does not receive enough scrutiny.
I will save the analysis of baseball vs. bucket vs newsboy (please don't wear a newsboy) for someone more qualified, but I am here to advocate for foregoing a hat all together.
I personally don't golf with a hat. This is for several reasons the most of which is that I have a large head (literally, not figuratively) which makes finding hats that fit appropriately very difficult. Secondly, I tend to perspire when I exercise so a golf hat would need to be semi-disposable as it would only last about a dozen rounds.
This is not to say that I don't buy or collect hats and visors from courses and tournaments, I do. But I keep them in my locker at the course or closet at home. I will also fully admit that when I did golf with a hat there were more than a few questionable choices, the most of which was probably the Ping "Gallery" hat from the early 90s.
When looking at pictures of professional golfers in previous generations hats were much less commonplace. The images of Palmer on the tee in a cardigan ripping a heater or Jack storming 16 at Augusta in '86 There were no hats in sight. Watching Rory McIlroy represent Ireland in the Olympics without a hat created more than most would expect were it not that hats have become a part of the current golf uniform. (Though the reason for the hat free event is less inspirational than you may think.) Even in CaddyShack the majority of the golfers didn't wear hats on the course. But the move still found a place for golf and hats to be a long lasting joke.