But as I've noted, none of these people (scientists, researchers) said they were trying to construct a "photon-only" theory. Electromagnetism and gravity have to account for masses with charge, but photons are massless. Wikipedia has a reasonable entry on "unified field theories", which does not mention a theory constructed entirely from the interactions of massless photons.
A "photon-only" theory is a misconception, therefore, of what their theories actually were.
A "photon-only" theory is a misconception, therefore, of what their theories actually were.