My expectation would be that getting the laundry into and/or out of the average commodity washer & dryer might be harder than you think. Robotic dexterity is very limited, and clothing can move and morph in all kinds of unexpected ways.

I'm sure a custom industrial-scale solution could be designed, but that still leaves the problem of folding. I suppose a compromise might be partial folding, like having the machine gently 'stack' the clothes in a return basket to minimize wrinkles.