I grew up with science fiction stories that grappled with the speed of light, sometimes treating it as an inviolable barrier and sometimes as an inconvenience to be papered over in the interests of advancing the story. Viewed as a natural law, the inability to exceed the speed of light somehow comes across as a traffic ordinance that's begging to be violated. We know light can go slower, as it does through glass or water, for instance, so why not faster? Learning a little bit more about it as an amateur, I now gather it's more a question of light-speed as an inherent quality of a specific thing, like the length of a pencil, that only seems to have maximum and less-than-maximum manifestations because we're looking at it in more or less foreshortened perspectives, so to speak. So your pencil might look longer or shorter depending on your angle, but it's always as long as it is, and no longer.
My Great Courses lecturer used an analogy that leapt out at me. Drawn from an excellent 1965 popular textbook by Edwin Taylor and John Wheeler (Spacetime Physics, 1st ed., PDF link to 1st chapter here), the analogy is "the parable of the surveyors." The king asks his surveyors to figure out how far the smithy is from point "X." One uses a coordinate system based on true North, while the other uses magnetic North, so they get different recipes for "go so many feet East, then so many feet North."
But the two vectors we add to get to the straight-line distance can be nearly anything, depending on how we rotate the frame of reference. The analogy is to space and time as the elements that make up the speed of light: from some points of view, the distance will be one thing and the time elapsed another, but those two elements can change. What will never change is the speed of light. It's not so much that light isn't "allowed" to go faster; it's more like the fact that the smithy is a certain distance from "X." Would it be allowed to be farther? Sure, but that's not where it happens to be.
The way the lecturer puts it is that space and time are aspects of the same thing, and the speed of light, c, is the conversion factor needed to switch back and forth between them. Similarly, mass and energy are aspects of the same thing, and the speed of light squared is the conversion factor needed to switch back and forth between them. Why is one just c and the other c-squared? No idea.