What is your rationale for advocating for caution here?
It's a fair question - my concern is 'shallow' analogies. I can best describe this with an anecdote paraphrased from memory from one of Hofstadter's books.
He described a piece of AI research (in the 60s?) where they set up a rule system - like Prolog or similar - with the mapping 'sun <-> nucleus' and 'planet <-> electron'. Then they ran the rule engine and lo! produced an analogy between the solar system and atoms.
Now this is a shallow analogy, as there is only a very weak correspondence between atoms and planetary systems. Electrons do not actually orbit in the same plane, but in more complex 'orbitals', and they are better described as probability clouds anyway.
So while yes there is a _homology_ (I re-read the parent and realised they used homology instead of analogy) between these two systems, it does not tell us much. Is there some mapping between how water molecules scaffold the folding process and storytelling? Does narrative structure tell us anything about local minima in the folding surface? I doubt it.
I do not want to be too harsh here - reasoning through analogy is fun and can be useful, it is just limited in what it can do, especially the further apart the systems are.
I expect because it's overly reductive to the point of falsehood. Two sufficiently complex systems will likely exhibit enough parallels to form a useful analogy, but that does nothing to reflect the ways the systems aren't alike.
Analogies are like models, some are useful, but they're all wrong. Just because we can analogize between protein folding and narrative/storytelling doesn't mean that we can derive anything particularly useful about one from the other except maybe to give an intuition about complexity. The mechanisms and math behind protein folding and an analogy between that and storytelling doesn't necessarily give us any mechanism for or deep understanding into storytelling.