I don't understand. Why is a duration of months preferable? What is the benefit above storing energy beyond say peak-to-peak? I suppose you can flatten out seasonal variation, but that's not nearly as big of a problem.

To see the importance, go to https://model.energy/

This site finds optimal combinations of solar, wind, batteries, and a long term storage (in this case, hydrogen), using historical weather data, to provide "synthetic baseload". It's a simplified model, but it provides important insights.

Go there, and (for various locations) try it with and without the hydrogen. You'll find that in a place at highish lattitude, like (say) Germany, omitting hydrogen doubles the cost. That's because to either smooth over seasonal variation in solar, or over long period drop out of wind, you need to either greatly overprovision those, or greatly overprovision batteries. Just a little hydrogen reduces the needed overprovisioning of those other things, even with hydrogen's lousy round trip efficiency.

Batteries are still extremely important here, for short duration smoothing. Most stored energy is still going through batteries, so their capex and efficiency is important.

You can also tweak the model to allow a little natural gas, limiting it to some fixed percentage (say, 5%) of total electrical output. This also gets around the problem. But we utimately want to totally get off of natural gas.

I suspect thermal storage will beat out hydrogen, if Standard Thermal's "hot dirt" approach pans out.