Consciousness becomes conscious of itself, and the notion of other is born.
The sense of separation between those two births space.
The continued, sequential unfolding of that process births distance and time.
Time and space are thusly intimately entwined.
As to the question: Why must there be an upper limit to velocity, i.e., the speed of light?
Answer: That need not be. But if there were not, the notion of distance, and therefore space, and therefore the notion of time, would not exist, and so there would be no universe.
Special relativity is just that simple.
Dimensionality, then, is dependent upon space-time.
Acceleration through space-time alters the experience, the nature of that dimensionality.
Theoretical physics first must understand nature. Then, the equations are found to express that nature in the language of mathematics. Trying to derive the nature of things from the math is a folly. First, nature must be understood. Then, the math is found to express that. The math then further clarifies the understanding.