Why don't we use grey water to flush toilets? It can use water either from the bathroom sink or shower.
Honestly, I do. I've placed a bucket in the sink to capture waste water from washing hands, which is then reused for flushing the toilet after depositing... liquid contents in it. It saves a bit off the water bill and also made me realize just how much water I use up when washing hands... Of course I hide the bucket when guests come, it's too weird a thing - but in all honesty, I've wished many times for a system for…
Unless you live in a very water constrained area, it's pretty unlikely. In the US, plumbing for reclaimed water is available in some areas (purple pipes), and seems like an easier intervention, it's often used for landscape irrigation, which has easily accessible plumbing to retrofit. It can be used for toilet flushing as well, if that is plumbed separately from other fixtures in the building.