Hallucination does allow the AI to find novel connections outside the exact context of its training data. It also is part of how it can perform tasks that it was not explicitly trained for, such as creating a sentence about an elephant who eats stew on the moon, where every word should begin with a vowel. (The AI came up with: An elephant eats an oniony oxtail on outer orbit.) This is the paradox of AI creativity. The same feature that makes LLMs unreliable and dangerous for factual work also makes them useful.