Having some cheap long-term energy storage option is one way to solve that problem, but another is better power grid interconnection. For instance, Chicago could get solar power from Chile in the winter time to buffer out the seasonal variability. Or if they didn't even want to have to maintain a smaller buffer to deal with day/night cycles, they could get solar power from, say, Algeria and Australia depending on time of day.
Power losses would be significant, but probably not all that worse than doing local electricity-to-hydrogen-to-electricity.
To quote wikipedia on HVDC lines:
> Depending on voltage level and construction details, HVDC transmission losses are quoted at 3.5% per 1,000 km
https://en.wikipedia.org/wiki/High-voltage_direct_current
An infrastructure project like that would probably be hugely expensive, but so is manufacturing lots of batteries or doing large scale hydrogen production and storage.