The argument that this cannot work is making the argument that NO storage technologies will be good enough, not that just Li-ion batteries won't be good enough.

There are thousands of different battery chemistries. It's an extremely strong claim that all will fail. And there are approaches beyond batteries that use only very common materials. For example, pumped thermal storage, where a reversible heat engine is used to separate heat and cold, then regenerate the work consumed by running off that temperature difference.