It's not really about light. It's not so much the case that the speed of light is itself special, so much as it is that light (in a vacuum) travels at a special speed. That speed is effectively that of causality, in the 'speed of the ability to cause' sense.

Trying to make conclusions about that by using simple analogies to light isn't likely to get you anywhere. You're not dealing with the actual thing you're interested in in the first place.