The assumption that the photon has 0 mass is still being tested, so it's not absurd to imagine it, and the universe may not look really differently if it was non-0 but small enough.

According to [0], the most accepted upper limit on a possible mass of a photon is m < 10^-14 eV/(c^2).

[0] https://en.wikipedia.org/wiki/Photon#Experimental_checks_on_...