You need a pump (and a filter) to recirculate the water, a heater for hotter water, and you need volume so that you can arrange everything so that they aren't t

You need a pump (and a filter) to recirculate the water, a heater for hotter water, and you need volume so that you can arrange everything so that they aren't touching and can all be washed. With a washing machine the size of half my sink, I'd be able to wash my largest pot and nothing else. With my small dishwasher, I can wash my largest pot plus almost everything else that's likely to need washing. Plus you'll want a seal that can keep in the steam, and some insulation to reduce the amount of energy you use continually reheating the water. Where does the lid go when you're not washing something? Does it lie flat on the counter next to the sink, taking up space you won't be able to use for anything else? What about the hinges? They'll be splashed with water repeatedly when you use the sink, so they won't last forever. But sure, you could build a dishwasher into a sink; it's not impossible.