Interesting that that's a feature of the water heater and not the tub. It has to travel through the plumbing all the way round-trip to the heater? You must have isolated recirculation plumbing to deal with the grey water, yeah?
Depends on setup, of course. If there's a central AC blowing hot/cold air through ducts, you're stuck using a grey water loop. But it is the least attractive setup...