The problem with this line of argumentation is it implies that autoregressive LLMs only hallucinate based upon linguistic fidelity and the quality of the training set.

This is not accurate. LLMs will always "hallucinate" because the size of the model they can encode is orders of magnitude smaller than the factual information they can contain from the training set. Even granting that semantic compression could reduce the model to smaller than the theoretical compression limit, Shannon entropy still applies. You cannot fit the informational content required for them to be accurate into these model sizes.

This will obviously apply to chain of thought or N-shot reasoning as well. Intermediate steps chained together still can only contain this fixed amount of entropy. It slightly amazes me that the community most likely to talk about computational complexity will call these general reasoners when we know that reasoning has computational complexity and LLMs' cost is purely linear based upon tokens emitted.

Those claiming LLMs will overcome hallucinations have to argue that P or NP time complexity of intermediate reasoning steps will be well-covered by a fixed size training set. That's a bet I wouldn't take, because it's obviously impossible, both on information storage and computational complexity grounds.