These diagrams imply that the incoming water to the heater is heated by drain water from the bath. But if you're filling a bathtub there's no warm water going down the drain. So the exchanger is useless here. And then when you're done and drain the tub the exchanger gets hot but the heater isn't filling any more. This device only really works in a shower situation, it seems.
And at that point you probably can "save the environment" more by not building a 10k sq ft mansion. But what do I know?