While your points are absolutely true as well, this is not what I got from the essay.
What I got from it, which is subtly different from what you say, but resonates with my experience a lot more, is that the brain has a habit of assuring itself it has the whole picture about a topic, almost to the point of delusion; it's kind of how the brain works; it generalises things into abstract patterns, and fills in the gaps for you. It's not until you're forced to externalise the information, and explicitly face the knowledge gaps you didn't even realise your brain had filled-in for you, that you realise how many of them there were in the first place.
Writing is a great way of a) spotting, b) attempting to fill / reflect on the gaps, c) realising you never had the full information in the first place, d) consciously deciding to fill in these gaps properly.
So yes, the process also helps you learn as a side-effect, but the point is not learning per-se; after all there are other ways to learn 'properly', where writing things down isn't strictly necessary. For me the main point of the article is the shock of how much implicit knowledge turns out to simply not be there when you try to prod it explicitly, and why writing things down is therefore such a good exercise/habit to cultivate in the first place, since trying to verbalise things explicitly on paper is an effective technique that forces you to 'prod' areas you didn't know needed prodding.