The question seems to me not why there is a speed of causality, but why the speed has this particular number. And it's not clear we know why that is, any more than we know why the proton mass is about 1836 times greater than the electron mass.
* https://www.youtube.com/watch?v=ZbGxXyqlhbU (FloatHeadPhysics on this)
One physics convention just sets its value to 1. All of those Minkowsky diagrams that we see are measured in light seconds on the space axis, in order to make c have the value of 1 space unit per time unit; so all of the graphical sheep, spaceships, cats, people, torches and stuff that are placed upon them are very much not to scale. (-:
Interesting. So c² would also equal 1. Which (in those scaled units) implies E = m.
This not only greatly simplifies the relationship but actually makes much more sense that way.
Not only does this clarify the relationships, but in many ways, these "natural constants" are an artifact from our past ignorance. Boltzmann's constant, in a way, is nothing more than a "conversion factor" that we hold over from the time when we believed temperature and energy to be two separate concepts. In the same way, the speed of light is an artifact from a time when we considered time and space to be distinct concepts, measuring them in distinct units, and needing a conversion factor (in units of distance/time) to map between them.
It's as if we would all collectively agree that the "up" direction, from now on, would be measured in floops, and the slope of a hill would be measured in floops/meter.
From a philosophical point of view, it's not just saying "measure time in units such that c = 1". It's saying "let's consider time to be a distance, and measure it in the same units as we do the other ones".
Here is an example. The charge of an electron is exactly the opposite of the charge of a proton, to within measurement error (like ten digits). This is simply something which has been measured, but physics has no explanation for why they are the same. Getting to the point, what is more likely: that a God created it that way in order to achieve His goals, or that there is some reason connecting the two charges such that they must be of exactly the same magnitude but we just haven't figured it out?
I'm putting my money on the latter. If there is an all-powerful creator, there is no reason to have fine tuning at all -- He could just force the desired behavior and outcome.
So I expect it would change a lot.
If the basic laws of the universe change, we'll be disincorporated before we have a chance to know it's happening, because it will happen at whatever the speed of light is in the new balance, and the chemical processes that make us tick will change to other chemical processes that don't actually work anymore.
In the new universe silicon based life might function. Or stars might not work anymore.
I don't think the numbers independently are valuable, but together the constants of physics are tuned to support life. To be honest, I dislike the Anthropic principle as a generalizable cop-out, but it nonetheless works.