Sadly current "dishwasher" models are neither self-loading nor unloading. (Seems like they should be able to take a tray of dishes, sort them, load them, and stack them after cleaning.)
The problem is more doing it in sufficiently little space, and using little enough water and energy. Doing one that you just feed dishes individually and that immediate wash them and feed them to storage should be entirely viable, but it'd be wasteful, and it'd compete with people having multiple small drawer-style dishwashers, offering relatively little convenience over that.
It seems most people aren't willing to pay for multiple dishwashers - even multiple small ones or set aside enough space, and that places severe constraints on trying to do better.
Maybe "busbot" or "scullerybot".