One of the most basic premises of a good photograph is that it communicate, to the majority of people who view it, the message intended by the photographer. This is a complex desire, and many variables can contribute to the success of a photograph in achieving this. If those variables are not controlled by the photographer, they can just as easily fail for this lack of control.
The foremost of these variables that a photographer attempts to control is the path a viewer’s eye takes “through the picture”.
The ultimate goal of anything you define as a compositional element in a photograph is to control the way someone “reads” the photograph. This comparison to reading text is not accidental. If there are no compositional elements, like leading_lines to control how someone moves over the picture, their natural tendency will be to start in the upper left corner of the picture and move from left-to-right, then top-to-bottom, just as you are doing with this page of text.
Working from the basic premise that Art = Craft + Intention, there are three things that anyone should think about when deciding on composition and what to include or exclude from the frame.
None.