While I'm not exactly a fan of AI, it does make sense that the first things we're able to replicate with AI, however terribly, are intellectual things like art and writing. While AI might be able to understand how to wash dishes, it would need a way of interacting with the physical dishes to do so, which goes beyond something a computer program can do while confined to a computer.

I wouldn't be surprised if future dishwashers and washing machines end up having little cameras and sensors so that AI can determine how best to wash them, but if anything that feature would be implemented more for collecting your private information than for any real washing benefit. Plus you'd still have to load and unload the machines - if we wanted AI to handle everything, we'd need robots, which would be waaaay more expensive, and likely something only the richest would be able to afford anyway.