Personally, I think the person who cooks should clean the cookware and the kitchen. The incentives are then aligned, and at least for me, it makes me a much tidier cook.
Also, cooking can be fun, cleaning not so much. Separating cooking/cleaning duties just punishes the person who doesn’t get to cook.
Note re: mustard. It is not just an “other flavor,” it is also an emulsifier!
It took me a while before I learned this. Even if you’re not going for a mustardy flavor, a little mustard goes a long way in keeping the oil and vinegar from separating. Definitely recommend using some with basically every dressing you make.