It might come down to that they don't care (enough). They could probably do it if they had to (hire a lot of professional editors and authors to train models), but AGI seems more profitable and also a better "story" for investors than models that are good at writing.

Thing is, LLMs don't seem to be the right vehicle for AGI, but even if the nerds understand that, see above about profit perspectives and investors. These companies are under insane pressure to deliver the next super hit or be seen trying.