On the other hand ...
Sometimes the big names became big names because they are just that good. It is easy to later say, "I could've done that." But you didn't and neither did anyone else. Since this is a strong composition thread, I'll pick approaching shadow from Fan Ho. A photograph I really admire. Yes, I could replicate that shot. Technically, it isn't that hard. But he did it. He had it in his mind, brought a relative as a model, had her dress in a certain way, placed her at the right time, etc. He orchestrated all of it. For me it's brilliant.
https://dgeiu3fz282x5.cloudfront.net/g/l/lg7715.jpg
(No one could claim it to be as TDB - See Vaughn above.)
The only point is that a no name shoots same image without ever seeing one from the "big" guy and would not get recognition even, if it were viewed side by side. Is it wrong that HCB was not all that great? He is not god. Have you seen all his negatives? Neither have I? Why? Because his hit ratio was like 1 to a thousand, pretty much like most of regular photo Joe Does. Had ever a look at Magnums Contact Sheets? Sometimes I have hard time believing they released them, but at least they are a published proof of subjectivity of seeing.
You refer to someone taking a shot before anyone else. That's hog wash, how many photographs are taken every day world wide? Seen any measurable portion of them?
Fame puts a photo on wider display, but should never blindly justify its visual quality, yet it does, in spades. I like Fan Ho, but what he's done needs to be put in perspective of places, history and culture where he worked. By shear differential his images are easy to notice in the Western world. I won't take anything away from Fan Ho, as I think he had an elusive way of seeing and capturing what he saw, and done it with striking consistency without being repetitious.
There are many great photographers, there are countless more who, for one reason or another, are at best just capable of repeating themselves and their supposed talent dries out pretty quick, only proving they actually had none, but hit it at a right moment and lasted a few moments more. Reading some commentary from gallery directors on an exhibit is a great proof of what kind of bull this whole business is surrounded by. Yet it drives opinions on composition in a significant way.