I don't think writing is an "AI-complete" problem. It's just that the models are inefficient at it right now, due to training and/or architecture. Good writing requires thinking, reflection, and doing multiple passes. This currently translates to using a high reasoning effort and burning lots of tokens, but big AI labs like Anthropic are struggling with handling the load, so they're doing the exact opposite and finding whatever cheap trick they can to reduce token usage. One such trick is condensing ideas into as few tokens as possible, which in my opinion is one of the reasons Claude sucks so much at writing.