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The following is exceedingly speculative and some of the arguments are anthropomorphic, so read at your own tolerance level. It relates essentially to interpreting physical world in terms of information theory and possibly quantum measurement theory, instead of directly from quantum mechanics.
If we consider space or spacetime as a statistical construction, and there exists a lower discrete limit to time such as Planck time, there must in fact be such a speed limit (perhaps c or some multiple of c) which arises naturally, since the observer cannot perceive objects traveling faster than the finite rate at which he/she can calculate the metric relationships between spacetime points. Traveling faster than this limit would be like trying to have your cake and eat it too...you wouldn't be able to observe a faster than light object because you would not have the time to create the space backdrop from information received. Now there might be very interesting loopholes to this idea which could allow FTL in certain circumstances, particularly if space can be created at a rate faster than the speed of light as perhaps occurred in the early universe. A recent very interesting paper published a few years back did indeed find a speed limit for propagation of information within networks regardless of the speed of node-to-node transmission. Classical special relativistic effects might be re-interpreted as a type of "spatial blur uncertainty" phenomenon in a statistical space construction. This also immediately suggest the Lorentz transformation should also involve y and z coordinates, not just x cooridinate for very high velocities approaching c. Perhaps more interesting however is the types of such spaces that can be "created" by the observer statistically might also have deeper connections with gravity at large open scales and O(N) groups at small closed scales. The Euclidean space we generally observe at intermediately large scales has very simple and unique symmetric properties which might be expected to naturally emerge from a statistical construction of all possible spaces much as Bell curve emerges naturally from statistically independent random variables or Feynman many paths merge toward the least action principle. There are also most definitely dimensional (and likely topological) constraints for the perception of such a statistical space which might provide clues to how this could come about naturally...for example a random walker will return on average only a finite number of times over an infinite time to the same point in a 3d or higher dimensional open lattice, so it would be impossible for such an observer to create the metric of his/her space from transit measurements without additional assumptions, asymmetries, and restrictions upon which points he/she could observe over time. In fact, this is actually how we generally perceive our supposed 3D world (through a 2D limited interface). This would not be generally the case at very small (finite) or closed scales (O(N)) interestingly and could provide a guiding principle for the construction of specific gauge groups from Kaluza-Klein and string theories...where there exists none now. It is perhaps also a telling anthropomorphism that we perceive open 2D spaces in two different ways, as a 2D "photon current" screen like projection in front of us, or as a linear horizon-like projection photon current x radial distance upon the surface of our earth. The later is much less direct and the linearity or lack thereof is controlled by gravity, perhaps reaching ideality at a black holes surface. If there was a continuous/smooth connection between the two, this could form a new duality.