> Heating and other energy-intensive water uses in homes and businesses make up almost 90% of water-related energy use, while treatment, pumping, and conveyance of water and wastewater account for the rest.
That's 2% for everything which isn't heating water. Pumping is some smaller fraction of that.
Water heating is basically the poster child for “demand-response” technologies. You can easily heat your water a few hours earlier than normal with basically no consequences to the user. But you need to get reasonable smart about modelling people water usage, as people don’t tend forget or forgive a cold shower.
Regardless the point is eliminating the use of natural gas in heating water is itself a benefit.
Summary the more hot water you use the smaller the win is for tankless.
Other thing I've read and seems true is gas and heat pump water heaters cost about the same to run. I installed a heat pump unit five years ago. Works okay for two people. If you had three teenage girls and a wife that likes baths a tankless would be a better choice.