I have my own theory, which is not disproved yet: gravitational background noise slow down light a bit. Gravitation affects whole stream of photons in uniform way, not individual photons. Moreover, it doesn't change direction of photons, so no blur or scattering. My napking maths, which I did few months ago, tells that gravitational delaying should case effect of same magnitude as in red shift, (I did calculation for one frequency only, for proper calculation I need to know the temperature of the noise).
I think the main point of resistance is the incompatibility with observations. All Tired light models have been falsified: https://en.wikipedia.org/wiki/Tired_light#Specific_falsified...
If you're aware of a model that can fit some or all of our observations, please share it!