Hmm, good point, I guess I hadn't thought about it, but that does mean whatever residual heat is in the water draining does get transferred to the water coming in to the tank, which if anything means the heater is less likely to come on.

For showers definitely. But as someone astutely observed, washing machines (clothes and dish variety) pull a bunch of hot water, and then dump it out a half hour later, and then may or may not pull more hot water afterward, but never while they are draining. I guess there's an expensive reservoir for that and that sounds like more water damage waiting to happen.

So the only heat transfer you'd get there would be whatever heat capacity the exchanger has. And since the thermal conductivity is high, all it's probably done is heat up the air inside of your walls a little bit.

The best alternative to me seems like heat pumps, although you might also be able to scavenge heat to feed into your radiant heating system, or the cold air exchange on your furnace. The former seems more likely not to cause problems on hot days.