Is there a physics/mathmatical reason for the ultimate speed limit, (avoiding saying "speed of light"), to be what it is?
In a word, no. At least, not so far as we understand things at the moment.
There are a few constants (the speed of light, the charge of a single electron, and a couple other things) that "just are", as far as accepted models go. For some reason, or no reason, when the Universe came into being, these constants had these values. They could have had other values, and with other values, the universe would be dramatically different. As in "human life could not exist" different.
This brings us to the Anthropic Principle. We see the kind of universe we see because any universe we see must be consistent with the development of our sort of intelligent life.
I mean, if the speed limit was, say, 200,000 mps, or 1 billion mps, would anything happen other than calculations change and things go faster -- other than just the numbers get bigger? What if there was no speed limit -- light could move instantaneously? Would this "break" the universe?
Whether or not it would break the Universe, if you vary it much, we break you. Specifically, we break atoms as we know them, so your physical body and the brain that supports your intelligence ceases to be possible. There might be a universe, and there might be stuff in it, but that stuff might be either a dissociated mist of subatomic particles or it all collapses into one big lump in the middle...
Also, and I have to think on this a bit, I believe that if light moved instantaneously, our concept of having causes and effects, the idea that events happen in an order, with one leading to another, goes out the window. There is no time. No history. No time-ordering. You cannot be born, live, and die, because there is no way to differentiate the moment of your birth from the moment of your death (from the moment you were conceived, or from the moment your parents met, or from the moment the Sun ignited).
Considering the size of the universe, it seems that this speed limit is really, really, really, ridiculously slow.
Considering the size of your living room, though, the speed limit is really, really, ridiculously fast! Considering the size of atoms, it is even faster...
"Slow" and "fast" are measures only useful when considering some human goal - there's an implicit human-centric value judgement in those words. It seems slow, because you actually want to get over there, and the limit gets in your way.