That was the original thought until I went off on the tangent about saving the hot water in a separate tank from the bathtub after it is "used" for the bath allowing the heat to be harvested and the water to be re-used.
The original post is about leaving the hot water in the bath to use the energy to heat the house or help heat incoming water. The idea of an external tank made out of conductive material would eliminate some of the problems and also allow the water to be re-used for the toilet.