What the "greats" all do seem to hold in common are simply; the choice to enter, the talent for, and the will to succeed in photography as a business, nothing more.
For example, Ansel Adams could very easily have ended up as a concert pianist.
This is not to say they didn't get good at their craft.
HCB did though choose to self-promote. He chose to be in business, that's a lot of work.
I see it as a shame that one must succeed commercially to be considered a great.