All good, I was just trying to reduce it to three basic essentials without complicating side issues as the side issues seem to be quite capable of being sub-sets of the three prime elements. My contention is that all my three postulations are always present in any image capture and they tend to vary on a scale 0-9 (9 being excellent). The hypothesis I make is that any image can be backed by two of these elements strongly and pass even if the third element is weak. However if two of the elements are weak then the image struggles.For me the essentials are:
Your photographs must have something to say, preferably something new . This is the most important.
The photographer must develop a personal style to some extent and must master the compositional aspects of photography. This is vital.
The technical side of things should be under control , not the measurebating stuff like equivalence, which is just fun for gear heads, but the knowledge of why to chose a certain shutter speed or aperture and when to over or under expose etc.
A certain determination and patience to get the photograph you want and not settle for second best when shooting helps. ( waiting for the light to change of waiting for that moment when that monument you want to shoot is free of bystanders).
The photographer must learn to examine and really look at everything in the viewfinder before clicking the shutter.
Photograph for a purpose or project and be very clear what the subject of a photograph or set of photographs is. My best photographs always occur when I know exactly what I am going to photograph.
Luck has little part in creating good photographs.
Photograph to please yourself and avoid playing to the gallery( photo competitions, likes on Flikr). I know it is nice to get all those likes.
Most modern gear is up to the job so this is not very important. One of my own favourite photographs was taken on a 3MP Olympus compact. The content for me transcends any technical limitations od dynamic range and noise. Just look at the great stuff Kertèsz did on quite primitive gear in his early stages. Changing camera will not make you a better photographer I am afraid.
If you want to improve your photography it is better to see by visiting exhibitions or reading monographs to see what other photographers have done or do, rather than reading gear orientated photo magazines or visiting gear sites.
http://nigelvoak.blogspot.it/
From your well reasoned response I would summarise: Good Talent + Good Opportunity = Good chance of a great image and the gear used is less important.
I could also say that the best gear + a great opportunity would give a good chance of a great shot as well but for most instances would be classed as "lucky shot". But this allows the lucky owner of that shot to claim bragging rights which short of a string of great opportunities might be hard to repeat.