That doesn’t make a lot of sense, you don’t use the same set of cookware every time. Say you use a pot, put it in dishwasher A, wash it, now it lives clean here

That doesn’t make a lot of sense, you don’t use the same set of cookware every time. Say you use a pot, put it in dishwasher A, wash it, now it lives clean here. Next meal you use a pan, put it in dishwasher B, wash it. Third meal you use a wok, where does it go? You still need to empty a dishwasher at some point.