[pfdietz]

It's not difficult to understand.

The mismatch between supply and demand is a function of time whose Fourier transform has components at various frequencies. There will be a strong component around 1 per 24 hours, which batteries will be good for, but there will also be much longer period components (seasonal, or from rare extended solar and wind combined outages, so called "Dunkelflauten").

Hydrogen (or other e-fuels) are well suited to the latter. For those storage needs, round trip efficiency is far less important compared to minimizing the per energy storage capacity capital cost. That's because there will be many fewer cycles over which to amortize the latter (while the contribution of round trip efficiency to levelized cost of storage is not so affected.) The per energy storage capacity cost of hydrogen is two orders of magnitude less than that of batteries.

To see this effect in action, go to https://model.energy/ and get it to solve for the minimum cost combination of solar, wind, batteries and hydrogen to supply a steady power output in Germany. Then, disable hydrogen and solve again. The cost nearly doubles.