More to the point photons propagate. The inaccuracy (maybe photons don’t move the same way water molecules at sea don’t move with the wave) is in thinking that the photons constitute the medium for a light wave. Photons are the waves, and to the extent that they’re localizable they “move”. Better to say they propagate, which applies to both localized and smeared-out waves.
Then again, I’m still coming at this from my aforementioned perspective that QFT makes visualization a lot easier.