You can shuffle a deck of 52 cards, and be reasonably confident that nobody has ever gotten that exact shuffle (or probably ever will, until the universe dies). But at least in this case, we are sure that a deck of 52 cards can be arranged in any permutation of 52 cards. We know we can reach any state from any other state.

This is not the case for LLMs. We don't know what the full state space looks like. Just because the state space that LLMs (lossily) compress, is unimaginably huge, doesn't mean that you can assume that the state you want is one of them. So yeah, you might get a string of symbols that nobody has seen before, but you still have no way of knowing whether A) it's the string of symbols you wanted, and B) if it isn't, whether the string of symbols you wanted can ever be generated by the network at all.