This is part of why plans for a primarily renewable grid assume that hydrogen or some other heretofore untested system will fulfill the overwhelming majority of storage. Because none of the existing electrical storage mechanisms are sufficient for grid-scale storage.
1. https://iopscience.iop.org/article/10.1088/1748-9326/ac4dc8
https://www.visualcapitalist.com/chinas-dominance-in-battery...
https://www.spglobal.com/mobility/en/research-analysis/growt...
It is unclear if nuclear would fill the gap they calculated.
Wait, you say, natural gas? But natural gas is dirty. Well, in the US if we could magically remove all other sources of greenhouse gas emissions except for the natural gas power plants, we'd be at net zero right now.
There is no such thing as a 'moderate amount of storage'. The best you can get is pumped storage (if you have the correct geography for it).
Outside of that, sure, you can add solar/wind to the energy mix - does that invalidate my point? Does that actually support OP's point?