Strongly recommend you watch Hans Rosling's TED talk on washing machines to realize how automated it already is: https://www.ted.com/talks/hans_rosling_and_the_magic_washing...

That said, I do still understand your point.

With the ability for machine learning to recognize your dishes, cutlery and paper trash, a robot arm could pick up these objects while a pressure washer of hot water sprays and dries. Wrap this up in a box with a conveyor belt on the front and half the battle is done. Putting the dishes back in the cupboard is another matter. It seems like a robot would be easier to build than a big box that somehow integrates with existing cabinets and drawers.