Re: your morning shower example. People seem to make the mistake of setting the mixer valve to their desired temperature position, routing to the shower head,

Re: your morning shower example. People seem to make the mistake of setting the mixer valve to their desired temperature position, routing to the shower head, turning on the water, and waiting for the water to reach temperature. That takes a long time, and wastes water. Probably not 10s of gallons, in an ordinary house, but 7-8 would not surprise me. The more efficient procedure is to turn on hot water only, routed to the tub spout only, for ~15 seconds until water is flowing hot. Then move the valve to the desired temperature position, and divert to the shower head. This wastes about 2 gallons. A tankless water heater wastes zero gallons, but it requires a gas pipe to the bathroom.