When my whole-house tankless heaters both crapped out (the chimneys were installed with the wrong angle), it was offered as an option to get hot water faster. It was more expensive, though, and only came with the newer models, which were also more expensive.
My partner is having a gas tankless heater installed at his house today, replacing a 40 gallon electric. The annual energy cost difference is staggering. About $1700 per year for the electricity vs $200 per year for gas.
Yes, the tankless is more expensive to install - $6700 vs $4000 for a standard electric tank, but it will take less than two years to recoup the difference thanks to the energy savings.
Are many of you people in the American southwest or something? I have a gas tankless water heater, and while it’s a bit annoying that the water in the shower or sink take so long to get hot when first turned on, worrying about the extra cost of that water or saving it in a bucket and using it for some other purpose have never even crossed my mind.
My thought on recirculating hot water heater piping would be to tie the pump to the light switch or fan switch. You turn on the light when you enter the bathroom, so it has about a 10-second to a minute head start to get the piping hot. Meanwhile, you aren’t wasting heat when nobody is in the washroom. (Or go high-tech, put a motion sensor in the bathroom…)
Some hot water recirculating pumps have 24 hours timers so that only run at certain times of the day. So if you usually shower at 7 am, the timer could be set to run from 6:30 to 7:30. And again in the evening if you shower at night.
The tankless heater my partner got has a gaggle of options that probably make more sense somewhere with several of the heaters like an apartment building, including remote control panels for temp and circulation, and even a Wi-Fi interface to control it with an app. I’d imagine setting up an IFTTT routine to toggle the circulation pump when the lights are turned on in the bathroom with a “smart” switch shouldn’t be terribly difficult.