>What sort of robot would you need to load and unload a dishwasher, collecting and storing the crockery etc.? What sort of robot would you need to load and unload the laundry, fold and store the clothes?

https://www.inceptivemind.com/toyota-gantry-robot-hangs-ceil...

You might now counter that legs are easy and a solved problem, sure, I won't deny that, but the point is that you should try to think out of the box.