I doubt it'd save you from purchasing a dishwasher - those things are very efficient and not very expensive. Perhaps it'd save you from loading and unloading a dishwasher
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?
That's a good reason to use a dishwasher, and you should keep doing it. But the overall waste is small and people aren't going to care.
I'm not saying people who already have a dishwasher will throw it away. But a robot makes installing a new dishwasher much less tempting.
At my utility prices, it costs about 5¢ to hand-wash one serving (plate, pan, glass, utensils, and a bowl) with running water. That's not nothing, but it's dwarfed by the energy use of using the oven and the supply-chain energy and water use of the food if it includes meat.
People will casually waste 10x that energy without a second thought when they don't need to just because it's convenient, or because they're used to doing things that way.
The dishwasher looks more unfavorable if you're considering installing one in a small apartment or condo. Apart from the cost of the dishwasher, you need space to install it, and more cupboard space to keep more dishes, glasses, etc. For an extra 4¢ per person-meal, having your robot do the dishes buys you the convenience of skipping all that and having all your dishes clean and ready all the time.
Just use the shortest two cycle program while following the two stage powder suggestion by Technology Connections. Obviously, if you are American you have to make sure the water going into the dishwasher is hot.
Honestly I don't even bother with two cycles and just use a 45 minute program in a 45cm wide dishwasher while throwing the extra powder in there anyway because it is too cheap to care about the waste vs tabs.