I have a counter-hypothesis: If the universe did distinguish between photons, but we didn't have any tests which could distinguish between photons, what this physically means is that our measuring devices, in their quantum-to-classical transitions (yes, I know this is a perception thing in MWI), are what is adding the amplitudes before taking the squared modulus. Our measurers can't distinguish, which is why we can get away with representing the hidden "true wavefunction" (or object carrying similar information) with a symmetric wavefunction. If we invented a measurement device which was capable of distinguishing photons, this would mean that photon A and photon B striking it would dump amplitude into distinct states in the device rather than the same state, and we would no longer be able to represent the photon field with a symmetric wavefunction if we wanted to make predictions.