When I visited Japan, I saw many toilets that had a little faucet/sink built into the toilet lid, so you could wash your hands with it before it was used to fil

When I visited Japan, I saw many toilets that had a little faucet/sink built into the toilet lid, so you could wash your hands with it before it was used to fill the tank. However, I'm not sure how practical that kind of thing would be to do at house-scale. You'd need to have extra set of plumbing, plus storage tanks for the greywater (and probably pumps to get it there), among other extra things.