Japan has this... a common design is to have the bathroom sink drain directly into the toilet's water reservoir, so the grey water is used for the next flush. No changes to plumbing needed, since it's all built into the fixtures.

Admittedly, there is a bit of a psychological hurdle to washing your hands in the toilet, even though the water is isolated and perfectly clean. (This could be solved through clever plumbing, to separate the two fixtures.)

Example: https://www.reddit.com/r/mildlyinteresting/comments/9rabuk/t...