I shave my head almost daily, have you ever thought about going maintenance free dreadlocks4 litres? Wash is fine on a daily basis - more like 1 litre is plenty though in a small sink.
However, hair is difficult in a small sink, hence my need for a shower every few days.
I have never lived anywhere that has a shower, at home I bathe. Water, gas and time consumption would be horrendous if I did that every day.