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Writing is for people, not compilers, and people don't like reading the same thing over and over yourself. Good writers don't repeat themselves simply because it's boring (except, of course, in situations where it makes sense to repeat yourself for some specific purpose, but I digress)...
Also, it's not fair to say that there is no leverage effect from writing. As a simple, obvious example, I leverage earlier blog posts that I've written in later ones. This saves me from having to re-explain older concepts, and allows me to reach into more complex concepts, since I have already explained the simpler concepts that the later elaborations rely on.
Finally, it's worth pointing out that the purposes of writing, piano-playing, or coding, are different. Coding is generally a utilitarian activity, aimed at achieving a practical purpose, that can be sped up profitably. Writing and piano-playing are more like entertainment. It's as pointless to speed up piano-playing as it is to speed up a dance.