The following is exceedingly speculative and some of the arguments are anthropomorphic, so read at your own tolerance level. It relates essentially to interpreting the 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 from finite information acquired over time, 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 perceive 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 could also argue, FTL is possible just not directly observable in this scenario. If c is the actual speed limit, one experimental effect one might expect is mixing of x,y, and z coordinates at speeds close to c, so that there should also be a y/z contraction as well as a Lorentz x contraction.
Perhaps more interesting than setting a simple speed limit however is that the types of such statistically determined background spaces which 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 intermediate scales between these two extremes has very simple and unique symmetric properties (rotation, translation, inversion invariance) which one might expect 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 for example approximate an observer who can collect only finite amounts of information about his space over time as a random walker who can observe one space point on a space lattice per unit time. It is a well know fact that on a infinite lattice higher than two dimensions, the observer would only return/observe any one point or transition a finite number of times despite an infinite time for observation, and would thus be unable to statistically determine the metric of such a space! 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 screen like projection in front of us, or as a linear horizon-like projection times a radial distance upon the surface of a gravitating body. The later is much less direct and the linearity or lack thereof appears limited and controlled by gravity reaching an absolute on the surface of a black hole where the observer and his reality is completely flattened. If there was a continuous/smooth connection between the two, this could form a new duality.