That’s the exact opposite of how most robotics are going for more specialized machines, not less. It is an interesting prospect, but what would be saved in space would be lost in more energy and water used (not to mention hygiene, we’ve used our dishwasher a lot more since we have had a kid to disinfect).
Are you sure a set of robot arms, trained over many generations to minimize motion/water/energy use, while also minimizing dirty dishes, would necessarily use more water/energy than a dishwasher?
What if the dishwasher is sometimes run half-full?