Since I have thought about a photon-only universe for about 40 years now; I might be able to sum up the major incompatibilities with other theories. This may help in judging
Quantum Mechanics theory is not compatible with every photon-only hypothesis I know.
Reason: QM uses particle exchange as the mechanism for transfer of forces. Photon-only concepts use fields of force that operate over distance as the mechanism for transfer of forces. This spooky action-at-a-distance requirement leads many to discount the photon-only universe concept.
Einstein's theory of relativity is not compatible with photon-only hypothesis.
Reason: Relativity phenomena happens naturally in a photon-only universe but only when space and time are fixed in the classic sense. In Einstein's theory of relativity, space and time are variable. In a consistent theory there can not be two different causes for the same phenomena.
Black Hole theory is not compatible with photon-only concepts.
Reason: Black Hole theory allows for a singularity where the force of gravity is strong enough to reduce the frequency of light to zero. In a Photon-Only universe mass is nothing more than electromagnetic change. No frequency; no change. No change; no mass. No mass; no gravity.
The Big Bang theory is not compatible with Photon-Only concepts.
Reason: The Big-Bang theory has the universe essentially spring forth from nothing or a very small Black Hole where gravity is either infinite or almost so. This would prevent the existence of mass, as per the Black Hole problem.
There are others I am sure, that don't come to mind at the moment.