The key is that the volume of the dishwasher is small, and in fact it has heating elements (plus insulation) to raise the water temp, so it can recirculate that

The key is that the volume of the dishwasher is small, and in fact it has heating elements (plus insulation) to raise the water temp, so it can recirculate that hot water (mixed with soap). I can imagine a bathroom with a drain (mine in fact has a concrete floor and a drain, so I can mop the whole floor into it) but there's no way to recirculate (or heat) water sprayed all over it, so the waste of water and energy would be huge.