Certainly "composition" can be taught, I said it never should be taught to aspiring artists, only an uncreative person would do that. Compostion as an artist has nothing to do with rules, guidelines, design elements, et al, it is done by feel and intuition. Don't take this view as that one should not have a strong understanding of art history, specifically the history of photography, but that should not influence how one works.
You say "Applying the elements of design or composition never results in clichés because there are so many possible decisions to be made that one cannot help but decide on a personal basis."
Our approach to photography is vastly different, with this approach one may make a good picture, perhaps something quite clever, but because you have choosen "the way" you have made something more superficial than one is capable of making, it does not come from the heart and soul of who you are and an ongoing interaction of your world; it came from choosing a style and the resultant will most likely never stand the test of time and live with the greats.
As an aside, were you serious about saying "Photographic associations" have defined what composition is or is not? It can be hard to discern tone on the internet...