Writing & Theory of Mind
Just had a profound thought that when you write you basically do "user thinking."
You're constantly thinking what would the person reading this think and how can I tweak this to be clear for their understanding. You have to have theory of mind of them. This is extremely clear when writing to a single person, especially a boss or similar that you're trying to convince of something.
It follows then that if someone was a really good writer, or tweeter they might be a good product person because they've honed a theory of mind of other people toward what they want.