How about integrating the cleaning mechanism into the dish cupboard so they don't need to be moved at all?

This exists. It's called dish drawers. Two mini-dishwashers in a unit with the idea that you will take your dishes out of one, use them, and put them in the other. When you need to, you run the dishwashing cycle in the dirty drawer. It does seem a little silly, but isn't storing your dishes directly in the dishwasher far more efficient than either manual or automated unloading?

You could build fully humanoid robots that solve every problem generically, or you could solve the sub problems much more efficiently - I don't know why everyone is all in on the hardest problem when in software and hardware we find that the "solve everything" tool basically doesn't work, because solving everything is usually solving nothing very fast.

You can buy a camera, portable music player, handheld gaming console, eBook reader, dumb phone, calculator, etc to solve each sub problem efficiently. Or you can buy a smart phone that generically solves every relevant problem. What direction did you take and how is life with it?

Those are all digital bit operating items that can be put into one box, the physical world doesn't work like that.

What makes the physical world different in this context? Isn't it things that humans are currently doing that we're automating away? Why not a human-like (in terms of capabilities) machine so it has similar flexibility?

Atoms are harder to reorganize than bits, undo is not an option because of entropy, game over means you are dead.

Yes, and my point is that human like is so difficult that solving lesser problems is a much more tractable approach.

I don't think most people would want dozens of task specific robots in their house it would be far more economic to have a single general purpose robot that can use pre existing tools and methods.

Right, I am saying that the fundamental design of household objects need to change to allow much simpler maintenance without humanoid robots.

I think its easier to build a dish washer that can stack plates from first principles than humanoid robots. The cultural shift is the harder part.