LLMs are useful because (and inasmuch as) their output generally reflects coherent reality.

And their output does, usually, reflect coherent reality.

The problem class of "properly operating program emits output incompatible with coherent reality" is something that is reasonable to put under its own term, considering it's a new class of problem.

In other words, I think you misunderstand the language others are using. "Hallucination" doesn't refer to an "error" in the sense that crashing is an error, it refers to a situation in the problem class above, which is compatible with it working correctly every time.

> it doesn’t “think” it predicts the next token.

I never said it did. And I agree that LLMs don't "think". That said I am fully willing to go to bat arguing "thinking tokens" is a perfectly fine piece of jargon. Metaphors are completely acceptable parts of language, and contextual meaning is something grasped by everyone including the pedants who pretend not to.