Your assumption that we need that much storage is simply wrong. This pops up in just about any article on HN mentioning batteries. Somebody will jump to the wrong conclusion that we need to provide massive amounts of battery storage and that therefore we need coal/nuclear/etc. (i.e. really expensive ways to generate energy) because buying so many batteries is obviously stupendously expensive. It's a popular argument with nuclear proponents and with the fossil fuel industry.
The reasoning roughly goes like this: wind and solar capacity varies because wind doesn't always blow and the sun doesn't always shine. This is very obviously true of course. Except these effects are local, temporary and typically result in a reduced capacity rather than a complete collapse. You always get some output out of solar panels (except at night). And wind turbines might stop spinning but it's extremely rare for that to be a continent wide thing. Offshore wind is pretty reliable. Also these effects are kind of predictable via weather forecasts so we can plan for them. Same with seasonal patterns. Simple cables rather than batteries are the key technology that we need. And we mostly have that in place already.
The grid connects power plants via cables. So, we can compensate for local dips in power with remote peaks. What matters is the collective performance of the grid. That still fluctuates but not nearly so dramatically that you'd need a lot of battery. E.g. the European grid is very connected. So, you might get power from Norwegian hydro, North Sea offshore wind, German on shore wind, solar plants in Spain, France, Germany, etc. or any of the gazillions of solar panels on people's houses. And of course there are coal, gas and nuclear still on the grid as well (for now).
All of that failing 100% at the same time is simply not a thing. Not even close. It's not something grid operators plan for. It might dip by 20-30% but it might also peak by that much. And it's likely to average out over time in a very predictable way. All that means is that we need to have a little more capacity. 2x would be overkill. 1.2 to 1.3x plus some battery will probably do the trick.
Batteries on the grid are intended for and used exclusively for absorbing short term peaks and dips in both supply and demand. Short term as in hours/minutes; not days or weeks. They are very good at that.
This is why modest amounts of lithium ion batteries are being used successfully in various countries. These batteries can provide large amounts of power (MW/GW) for typically not more than a few hours. The reason that is cost effective (despite the cost of these batteries) is that taking e.g. gas peaker plants online for a few hours/minutes and then offline again is expensive and slow. And of course with cheaper wind and solar providing cheap power most of the time, gas plants are increasingly pushed in that role because they are more expensive per kwh to operate. Gas plants on stand by still cost money. And turning them on costs more money. Batteries basically enable grids to have fewer (and eventually none) of those plants. These gravity based batteries have the same role. It's a cheaper alternative to lithium ion batteries.
Currently, clean energy is the dominant form of energy in many countries already (e.g. Europe, China, parts of the US). In some countries it's well over 50%. This proves the point because these grids don't feature a lot of battery currently and the combined capacity of peaker plants (i.e. not operating continously) is far smaller than the presumed need for batteries. If you were right, these countries would be facing massive blackouts all the time as their dominant form of energy disappears for days/weeks on end. That's obviously not a thing.