World famous (OK, maybe not so much now, but he was famous for reals back in the 1970s) but of a category for which there's only one famous person.
Cousteau was a world-famous underwater photographer . . . actually the only famous underwater photographer.
Another example, also from the 70s (sorry): Marcel Marceau. A world-famous mime . . . actually the only famous mime.
I'd also like to include Jane Goodall, world-famous primatologist . . . but there's also Dian Fossey.
Jack Chick was a world-famous religious cartoonist . . . actually the only famous religious cartoonist. But that seems like too offbeat a category, it's like we're saying he's the only famous Jack Chick. Cos really his job wasn't "religious cartoonist," it was just being himself.
Jimmy Carter was a world-famous peanut farmer, and there were no other famous peanut farmers, at least not since George Washington Carver. But being a peanut farmer was not what Carter was famous for. Also, maybe "peanut farmer" is too artificially specific.
The guy who wrote All Creatures Great and Small was a world-famous veterinarian, and I can't think of any other famous veterinarians, so I guess that works. To my taste, though he doesn't quite fit into the template. It's something about him being famous for writing. Cousteau and Marceau were famous not just for publicizing what they did, they were famous for what they did itself, if you know what I mean.
Then there are people who are so damn famous they're unique. Jesus is the only Jesus. But that won't work. The point is that there should be others of the category, just not other famous people of the category.
And it won't work to take people like Danica Patrick or some other such trailblazer. Patrick's category is "race-car driver," not "female race-car driver" -- and there are a lot of famous race-car drivers.
Ummm . . . Jackson Pollock is a world-famous drip painter, and indeed the only famous drip painter. But it's not clear to me that "drip painter" should count as a category.
To return to the 1970s for a moment: back then Carl Sagan was a world-famous astronomer, and the only famous astronomer. Since then there's that other astronomer guy who had the TV show, and before there were Copernicus, Kepler, Gauss, etc., so I guess Sagan doesn't work.
That guy Joseph Joanovici was a world-famous scrap-metal dealer, at least for anyone who read Il Était Une Fois en France, and I can't think of any other famous scrap metal dealers, but I guess we can't really say that Monsieur Joseph is really world-famous.
Hey, here's one I just thought of . . . Tony Hawk! At least, he's the only famous skateboarder I've ever heard of.
I feel like there must be lots more people in the class Jacques Cousteau that I can't think of. Can you help?
P.S. See here for more objects of the class "Objects of the Class."
P.P.S. Some good suggestions in comments. Also, I thought of another:
Nate Silver, world-famous statistician. And there are no other famous statisticians. OK, maybe Bill James, but that's it.