> I certainly can't see a way for LLMs to generate "smarter" text than what's in their training data.

Their training data contains much more knowledge than any single human has ever had, though. If they had equivalent linguistic, understanding and reasoning abilities to a human, but with so much stored knowledge, and considering that they also win in processing speed and never get tired, that would already make them much "smarter" than humans.

Not to mention that LLMs are just the current state of the art. We don't know if there will be another breakthrough which will counter the limitation you are mentioning. We do know that AI breakthroughs are relatively common lately.