I don't have that strong a background in photo history, but I do have a background in painting history, and with a couple of exceptions, virtually every great painter had extraordinary instruction. If you have, say, a 98% correspondence between strong teaching and great artists, I think you might at least suspect a connection.
I don't believe this is the case at all. Read Why Art Cannot Be Taught
by James Elkins. What happens, in fact, is that connections are fabricated, usually by outside parties, in order to support pet hypotheses regarding "artistic lineage". Elkins demonstrates how art schools are quick to cite students who have become successful as validating their programs, when, in fact, many of these students were drop-outs. In the case of photography, starting with Callahan, many "name" photographers turned to teaching rather than commercial work for their income. It then became a convenience to say "I studied with _____" as a way of claiming legitimacy, whereas the actual connection is suspect at best. I've done that myself. Callahan himself had grave doubts as to the efficacy of teaching.
Let me expand a bit on this. Prior to the Modernist period (roughly from Manet on, opinions differ on either side, but Manet is a good median), there was a strong tradition of craft (grinding pigments, cooking up and preparing grounds, drawing from plaster models and life, etc. etc.) which was arguably a necessary prelude to creating a painting that wouldn't self-destruct in a generation. The academies were not loci of strong creative influences but tech schools. Apprenticeship was a possible opportunity for an acolyte to learn from a strong master and there may be cases where this can be demonstrated. That, however was then. The modernist period was supported by ready-to-go technology - portable tubes of paint, commercially prepared canvases, etc. This had the effect of helping to unhook painters from the academies, which for the aims of Modernism, were increasingly regarded as onerous and unnecessary. Artists were increasingly essentially self-taught and if exposed to a strong teacher, were as likely to take an antipodal position as not. So, if one goes down the list of "great" Modernist painters it is hard to discern influences since, by definition their work was characterized by a violent break from the past. Who then taught Picasso Cubism? Mondrian De Stijl
? Who was Van Gogh's mentor? Can one really find traces of Thomas Hart Benton in Pollock's drip paintings? One could go on. In today's art education practice, Elkins, cited above, is hard pressed to find anything that students learn from their teachers. Maybe, if the school is marketing savvy, how to chat up influential people about art.
As regards composition in particular. There exists an academic practice (rules, non-rules, koans, and superstitions) that seems to have its center of gravity in commercial photo schools and which is preserved by camera clubs and individuals flogging workshops. I remember flipping through a book of ~50 years of Magnum photography and not finding a single example of "the rule of thirds". These rules break down in street photography practice, are irrelevant in post-modernist practice, have nothing to do with success in the marketplace, and are not even useful when the bounds of the frame move from the roughly rectilinear, as in panoramic presentation. Having said that, it's quite alright for an individual to develop a personal sense of what composition means to him/her, to sample from the plethora of "rules". etc. It's quite uncertain if "this" represents somethings that can be taught. It would seem that the individual develops a personal relationship in the realm of what we call "intuitive". What is nearly certain is that the results of a given image will violate someone's sense of "composition". The reactions will range from "boringly predictable" to "wildly unbalanced". Keep shooting, y'all.