Like literally nothing distinguishes this idea in boldness from other ideas except that its not the current mainstream view. Also, no experimental verification.
If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models without some other compelling experimental means of determining its presence. I believe folks are trying to figure this out, but at present, my money remains on spacetime being continuous. I don't know shit, but I expect good quantum gravity theories will need to be scale free.
In general I think this CA stuff is much less deep than it seems to be. You can, of course, approximate continuous differential equations with discrete difference equations, which is, fundamentally, what all this boils down to, in the end. It isn't surprising that with appropriate rules one can reproduce smooth mechanics at scales way above the discreteness scale.
The above entails that the speed of light is not quite constant, but rather energy dependent; c=f(E). The variation would be very small so detecting this is challenging. Myriad observational hurdles may prevent us from ever detecting such small variations but there are many reasons to posit such a model, most quantum gravity theories do so.
But it seems to me that the acid test, as always, is successful prediction. If one day a digital model makes a prediction that is experimentally demonstrated, and not accounted for via other models, then there might be more support for this approach.
Wouldn’t those simple rules be mathematics? It’s very hard for me to see how the world isn’t made of math. Then again, I am a Pythagorean.