Yes, it is an axiom for relativity, and thus for all modern physics. We have no _absolute_ proof for it, but everything we know suggests so, which is as good as things can get.
As to “why”… this kind of metaphysical questions will most likely never find a true and proper answer. Even if it some day follows from an even more basic and yet more general theory of nature, this just moves the goalpost. In the end, we can at best make guesses.
For example and not entirely serious now, if one believes that the universe is a just an elaborate simulation, then it might just be there to limit interactions and thus computational complexity; or some programmer used a data type of fixed size (which also somewhat explains Planck lengths).
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