I think it's very possible there are other species that use "oral history" to convey information to their children, like whales, dolphins, etc., so it's not "safe" -- again just IMO -- to consider it uniquely human.
I guess it is hard to say… if you looked at humans in any random moment when we’ve been around, I suppose we’d look a lot like dolphins (not making much increments progress generation-to-generation).
But, it does feel like there’s something in our storytelling tendency, maybe just a quantitative difference (we do it a little bit more and some up with slightly better summaries) that creates a qualitative one (positive feedback loop in our ability to reason about the universe).
From that point of view, writing is just an iteration of the loop. A big one, though.