Not a physicist, but I know that there are physicists who disagree with that. See: Roger Penrose and CCC.

I'm not sure if Penrose suggests that time stops once there are only photons left. He says it is equivalent to the situation at the Big Bang and time certainly didn't stop there. In fact, in his conformal cyclical cosmology spacetime goes on indefinitely but just reboots regularily.

Right,but I think the idea implies that time is different, not that it keeps going on as normal. Honestly not sure though.

Apparently time requires mass...