I'm no physicist particle farmer so take this opinion for what it is worth.

Using the phrase "Speed of Light" is such a misnomer I believe it actively causes harm and makes some things in physics more difficult to understand than they otherwise would be. Why should light's chosen speed have anything to do with, well, anything at all? Why should time travel being impossible be related to light? Why should our ability to travel have anything to do with light? Why should time dilation give a fig about light?

The answer is none of those have anything to do with light or its speed. Whatsoever. Our universe has a speed of causality. The maximum speed at which changes in the fields that make up our spacetime can propagate from one quanta, one point, of spacetime to another. This is a physical property of the universe itself. Putting everything else aside if light did not exist all of those other effects would remain unchanged. The maximum speed anything with mass could travel would not change. The need to adjust the clocks of GPS satellites due to time dilation in a gravitation field would not change. Light has nothing to do with it.

Light travels at a maximum speed because having no mass the laws of physics require it to do so. Light speed is a side effect. It is not the cause or source of the things attributed to it.

I don't know if Speed of Causality is the right phrasing but we need a better one. Quantum physics is brain-breaking enough, no need to go confusing the matter by inferring that the speed at which light travels is the cause of other phenomena.

A further aside

All metaphors, analogies, and simplifications are by necessity imperfect. Most people cannot understand anything without first grasping a simplified version of it (I certainly cannot). A proverbial hook on which to hang one's mental hat. The more abstract the concept the more concrete the path to understanding needs be.

Imagine our universe - our spacetime - is made up of an uncountable number of tiny quanta or points. There is no such thing as "between" these points. They are existence itself. Imagine further that each point can only transmit or receive changes in fields from its immediate neighbors at certain defined steps in time. In other words the clock ticks, everyone exchanges changes like white elephant gifts, then sits back down to process what they've got and plan the next move. None of them can take or hand over anything until the next clock tick.

Thought of this way it makes complete sense there should be some maximum speed during which the current point applies the rules and the results are propagated to its neighbors during the next step. The total time it takes for these ticks to happen over some distance is the speed of causality over that distance. The maximum speed at which each neighbor can hand things to the next neighbor in a long bucket brigade.

Now does our universe actually work this way? I have no idea. Probably not. It is just an analogy. Hopefully someone with greater understanding will come up with a better one.