tankless heaters use slightly less energy, but they use it in a really annoying way. the optimal design for a heavily renewable grid is a heat pump water heater with a tank

The optimal design for a heavily renewable grid is solar water heating a tank in home whenever the sun shines, falling back on a heat pump water heater with a tank.

That's for maximizing energy efficiency. Tankless I think might be a tad bit more easier and cheaper to implement than this.

Regardless the point is eliminating the use of natural gas in heating water is itself a benefit.

That's only optimal if you know you'll need 100% of the heated water (or have a way to store it). While photovoltaics are going to be less efficient than direct water heating, you can direct the energy to other uses if you don't need more hot water.

Large tanks of water are about the cheapest way we know of to store energy. Batteries store more energy, but are extremely expensive.

Yes, but that only matters if we can easily consume that energy. If we need the hot water, then that's easy—no conversion loss. Otherwise, it gets trickier, especially in a small-scale setting like a home.

All homes use at least some hot water for showers. In many climates they can use a lot of energy for heating which means a very large tank could be useful in winter.

I read a study looking at the difference between tankless and tank water heaters.

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.