I generally agree with your comment, but not on this part:
parroting the responses to questions that already existed in their input.
They're quite capable of following instructions over data where neither the instruction nor the data was anywhere in the training data.
They're completely incapable of critical thought or even basic reasoning.
Critical thought, generally no. Basic reasoning, that they're somewhat capable of. And chain of thought amplifies what little is there.
In many cases the key exchange (kex) for symmetric ciphers are done using slower asymmetric ciphers. Many of which are vulnerable to quantum algos to various degrees.
So even when attacking AES you'd ideally do it indirectly by targeting the kex.