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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. One experimental effect one might expect in such a scenario is that the y and z coordinate should also ultimately contract (as does the x coordinate) for very high velocities approaching c.

Perhaps more interesting however is the types of such spaces that could be realistically measured and determined by an observer might 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 scales between these two extremes has very simple and unique symmetric properties which one might be expected to naturally emerge from any statistical construction of all possible spaces much as Feynman many paths merge toward the least action principle. At very large scales, however there are most definitely dimensional (and likely topological) constraints for the perception of such a statistical space. We can approximate an observer who can collect only finite amounts of information about his space over time as a random walker who can observe one point on this lattice per unit time. It is a well know fact that on a infinite lattice higher than two dimensions, he/she would only return/observe any one point or transition a finite number of times despite an infinte time for observation, and would thus be unable to statistically determine the metric on the space he/she is observing. For generally finite (and thus closed and small) spaces, this is not a problem however, and it is perhaps the reason why we get interesting gauge groups like SU(3) etc at at small scales whereas we perceive simple and limited 2D projection of a 3D space at larger scales.

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.