To me, any discussion on this subject has to start with the acknowledgement that there isn't one type of photography, and that the elements that may (or may not) make "strong composition" - or even simply "composition" - will vary according to each.
Street photography, wedding photography, photojournalism (from social documentary to war photography), "fine arts" photography, portrait photography, fashion photography, landscape photography, still life photography, etc., each have, not rules, but certain codes, a particular syntax (or syntactic elements) that defines it. Some have more codes than others - wedding photography, for example, is much more codified than street photography, essentially because of clients' expectations.
These codes, or syntactic elements have changed through time (there is street photography after Frank and there is street photography after Eggleston), as they are modulated, transformed, transfigured, reinterpreted by the particular eye, imagination of photographers, who sometimes add new codes - like Cartier-Bresson's geometry - that are then left to be modulated, transformed, transfigured, or completely dismissed.
Trying to define "strong composition" without acknowledging that there are many different types of photography each with its own compositional parameters is like trying to define "strong composition" in music and putting in the same basket jazz, classical, minimalism, hip hop, rock, ambiant electro, blues, R n' B, disco, K-pop and prog.