I have a dishwasher and I still usually just hand wash. It takes about 10 seconds to wash a dish.
The side benefit is all your dishes are always available. With the dishwasher, up to one full dishwasher load are dirty at any time, which means you need more dishes and more cupboard space than someone without a dishwasher.
If the robot is going to clear your dishes and wash them for you right away, what's the dishwasher for? To save the robot 10 minutes?
Mostly to save water and energy. I have a hard time believing the robot would be more efficient washing dishes by hand.