Ok, I get the seed/state space vs. cycle length bit. So it can theoretically generate all of the permutations of a shuffle if you re-key/re-seed periodically. But you can't guarantee that it actually will, right? It is possible that, for all 2^128 keys, and in all 2^128 cycles there are some shuffles that AES will never generate (in other words, some sequences of 52 numbers that will never be generated) so you effectively have a 0% chance of hitting them.

From a cryptanalysis standpoint I think that's consistent -- the probability of generating any particular single shuffle is astronomically low, so the difference between the actual probability and 0% is probably outside the realm of what's computationally feasible. But with something like MT19937 I can show that its at least possible for every outcome to have a non-zero probability. Perhaps this is just interesting academically, but maybe not if you're actually playing a card game for instance?