But it producing an average of its inputs does not mean that it produces writing of average quality. That would only work, if writing was random, like the proverbial monkey on a typewriter.

Instead, average quality writing is already very deliberate. Any human that writes is at least superficially aware of what they want to convey and to what group of people. An LLM can try to emulate that, and particularly successfully so when it has a text from an actual human writer on this topic in its training data. But it is incapable of the critical thinking necessary to actually decide in what order and with what level of detail to explain something novel.
Crucially, it does not understand things. It only produces patterns. So, it doubly cannot understanding what is necessary to actually understand things. What information you need to be provided before it clicks. And what information is just noise that distracts from the shortest path to understanding.