But, it is sort of common to observe the somewhat trippy fact that, unlike matter, photons don’t experience time passing, right? (Although, I will be honest, I could not ever really grok relativity like a physicist. However, I can enjoy the Lorentz factor going to infinity as v goes to c).
From my understanding, it's more correct to say that time is undefined for massless objects.
Through special relativity, our understanding of mass, gravity, and spacetime are linked. If something has no mass, then special relativity can't describe how gravity affects it's spacetime reference.
Remember, however, that this explanation is based on the mathematics that explain the observations we've made or theorized. Just as the map is not the territory, the math is not the universe.