I was looking around for an answer to the question of why the speed of light (or other massless particles) is finite. The best explanation I could find is here:
Your question is really asking how fast a universe which lacks Newtonian time can run under Newtonian time. If you do attempt to run it under Newtonian time, you can indeed run it at any speed you like, including running through the whole of time instantly. Einstein's model lacks Newtonian time altogether, so it also lacks speed altogether and movement too: it gives us an eternal block universe where past, present and future all simply exist as a static block. Clearly it's difficult to think around such a model, so Newtonian time gets dragged back into it by accident whenever people try to explain how it hangs together through normal langauge, and that repeatedly introduces all manner of confusions. Many of the key words we use to describe things automatically smuggle in Newtonian time along with them, so you have to be continually on your guard.
I think what it boils down to is that light travels at the speed of time (and vice versa). The exact finite velocity is determined by the electromagnetic forces and they are what they are. If they weren't, we probably wouldn't be here.
Am I on the right tracks?