Good analogy. There's a flip side to it though. You can be a great comedian on the level of individual jokes, or short bits, but be unable to write a story. And you can be a great jazz musician when it comes to soloing, but be unable to write a song. Stan Getz was a famous example. So yeah, learning jazz by imitation and immersion (as one learns a language) is very cool: learning these hundreds of songs will most certainly teach you how to solo. But it won't teach you how to make a song. Not nearly as reliably. It needs something else, I don't know what.

I don't know quite what it is either, but I do know with certainty because it was my own experience that the act of inventing songs doesn't require any kind of experience at all, as some of my earliest memories as a child were riding in a car with a radio playing in the background, having some melody occur to me, and then being unable to get it out of my head. They weren't novel because they wouldn't have come to me had I not been idly listening to a lot of music, but neither were they just a slight variation on what I had been listening to.

I am by no means a prolific or genius songwriter, nobody would know any of my music, and I don't believe that any of it is particularly impressive. However I've always found the fact that it happened spontaneously way to be a source of wonder, and as I've aged as a musician its delightful to see the endless stream of new songs and that it doesn't seem to matter whether you're a prodigy when it comes to writing songs that impact listeners. It seems to be a fundamental aspect of the human experience.