"terry" wrote in message
All this heating sounds wasteful? What's wrong with a quick shower
then leave the couple/three inches of warm water in the tub to cool
down to room/house temperature before draining it in order to keep at
least that much energy within the structure.

Nothing wrong wit it. You have to balance the savings in heat versus the
energy used when it comes time to scrub the tub more frequently because of
buildup of minerals or scum from the standing water.