This is interesting, but I wonder what would present 4 of the many great photographers. I think that would need to be 4 that established a new direction for photography, that made the work of other great shooters possible. I've had a chance to re-think this, and will change one vote. Sort of.
Of the early workers, I think Fenton, Brady, Marville, et al., deserve equal mention: they used the camera as a new tool that exploited it's difference from drawing and painting. The tendency was explore one's world, and Cameron was doing this as was Fenton, et al. Just a different world. Photographers like Fay Godwin carried on this tradition.
At the end of the 19th C, as the choking effects of the Salons were suffocating good photography, PH Emerson ignored the Respectable and Setimental hacks like Robinson and set photography back on the tracks. Stieglitz followed this course, as did Strand: Emerson was the one that broke the ground. His work, I think, was fulfilled by Adams, the final blossom of American Neo Romanticism.
Weston, the Modernist: Photography's Picasso. Sheeler can't be discounted, nor Strand, but it's Weston on whom they all rest: Gibson, Erwitt, Avedon. Even Minor White and Eggelston follow in this vein
Eggleston: probably the only photographer -still- who made color pictures that needed color and simply weren't B&W pictures on color film ). Sander, yes, a romantic modernist.
The spot for Smith is for the perfection of the Essay; Kertesz, Brassai,Capa, HCB all were monumentaly important but it was Smith that fulfilled the direction they all were heading while beginning the direction to be taken by Salgado, Richards, Mark, and others. Smith shot people, yeah, but he changed the form.
Postmodernism ? Can there be a PostModern Photography ? I don't think there was. Probably the closest we came to a PostModern sensibility were ... well, never mind. That would just start a flame war. And only the innocent would be hurt.
The next Great Photographer ? We're still waiting. Probably someone who is able to ignore the Agonies of Post Modernism, and the Rapture of Commercialism. Probably a kid out there playing with a pinhole camera.