The author of this article, Gary Klein, also came up with the concept of the "hot water rectangle":

> To find the hot water rectangle, you draw the smallest rectangle possible that includes the water heater and all the hot water fixtures in a house. Then you find the area of that rectangle, divide it by the conditioned floor area, and express it as a percentage. If the hot water rectangle is as big as the conditioned floor area in a one-story house, the ratio would be 100%.

[…]

> Klein worked with Habitat for Humanity builder George Koertzen in Stockton, Calif., and helped him make a dramatic improvement in efficient hot water delivery by reducing the hot water rectangle ratio for the single-story houses he built. Before learning of the importance of clustering the wet rooms, Koertzen was building a floor plan with a 79% ratio. Then he saw the potential and got that down to 15% on his first attempt. Then 4% . . . then 2.5% . . . and finally, an astounding 0.8%!

* https://www.greenbuildingadvisor.com/article/the-hot-water-r...

This helps in making a more efficient hot water delivery system:

> When you think it through, it’s easy to see that hot water distribution suffers because of one basic problem. When 3 [US] gal. [11 L] of water spill out of my kitchen faucet while I wait for hot water, that tells me something about the volume in the hot water line between the water heater and the kitchen faucet. To waste less water, I need less water to be sitting in that pipe. That’s it. That’s the problem.

* https://www.greenbuildingadvisor.com/article/why-your-hot-wa...

To further reduce the amount of wasted water (those gets poured out of a faucet), a further optimization would be for the hot water delivery piping to be a full recirculation loop:

* https://srmi.biz/wp-content/uploads/2021/12/Klein-G.-2005-Ho...

* https://www1.eere.energy.gov/solar/pdfs/sda_saving_water.pdf

The hot water pipe would leave the heater tank, go past all the faucets in the house, and then feed back to the the tank. At the end of the loop would be a pump and a temperature sensor: when you (e.g.) wake up in the morning and want to start using hot water you would press a button to tell the pump to start. It would pull water out of the tank, and all the water in the pipes would be pushed forward. The water in the pipes would be cool because it was sitting over night, and that would be put back into the tank.

When the cool water was replaced with hot water the pump would stop (the sensor would know the 'flush' of the system had been achieved).

When you turn on the faucet hot water would come out basically instantly (there would be some 'residual' amount between the main distribution pipe and the small branch circuit to the faucet). Most of the water would to back into the tank to be heated up, so very little would go down the drain.

* https://www.youtube.com/watch?v=13h0L_GlOlI

* https://www.youtube.com/watch?v=1b8XaEygtKs

* https://www.youtube.com/watch?v=0FT9n_rLGsw

Some system do recirc 24/7, but this would be probably be more wasteful (esp. in residential) since you constantly have heat loss from the pipes. An on-demand press-button system would be best, and perhaps a timer-based system perhaps second-best (heavy morning and evening/dinner use).