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I didn't expect this question to end up as thread on its own. To be honest, I asked it to make the OP in the linked thread think about this issue, as I see no reason to bother, let alone get angry, because some photo has no good composition. It's a question that came to me when I looked at my shots and noticed that most of them neither have an interesting subject, nor a good composition. To me, there's always something that could have been done better, but I missed it and have to deal with the results. Personally, I think that moment>composition, but this heavily depends on the subject matter.
Anyway, it's nearly impossible to have a photo without any composition: As soon as you force the 3-dimensional out of the 360° around you into a frame with a given aspect ratio, the elements in it relate to each other in some way.
Recently, I worked with some school children (1st and 4th grade) on a photography project and handed them some disposable cameras. We headed out and I'm pretty sure nobody ever told them about composition, exposure, or anything else photography related. Still, they ended up with 27 shots per team (1 1st grader + 1 4th grader). A lot of these shots show nothing that anyone who hasn't been with us on that day would find interesting, but the kids thought about what they wanted to shoot/show. One reason, I didn't tell them about composition was to test my hypothesis that everyone has a basic sense for aesthetics. Here's a shot one of the 1st graders took of me with my camera, judge for yourself.