In case you're curious, this came up a few years ago in a discussion and at least at the time I checked a typical Hall-Héroult electrolysis smelter could last without power for something like 4 hours or so, maybe 5, and some countries did in fact use them as part of their electrical grid control. But they can't have power interrupted indefinitely because the pots are permanently damaged and require replacement or extremely expensive repair if the liquid metal completely solidifies in them. The molten state represents a significant thermal mass hence the hours of lag time, but it can't just be remelted from total cool down either.
I do wonder if an economical design could be made that specifically tried to enhance this aspect as a core design feature, some sort of vacuum insulation or the like perhaps to reduce passive thermal loss and bring outage time more towards 12 hours? But even at 4 apparently it can be good enough for moderation of some intermittent demand (which in turn means extremely cheap electricity). Using something like this as "energy storage" that is also directly economically productive seems worth pursuing though. Another possibility would be to investigate direct carbon extraction from the air, either for storage or to turn into fully synthetic net-neutral hydrocarbons. If the electricity is essentially free anyway, even enormously consuming processes like that could make sense.
At residential rates the cost is a few hundred a ton for energy. So not economic vs carbon reduction. But if you could get the energy for nearly free. It would be.
* Wind and solar, over-provisioned, will supply the generation.
* Batteries will provide peak-shifting and frequency maintenance.
* Grid upgrades / HVDC will even out regional variation in generation due to weather while flattening the duck curve.
* Variable pricing will lead to more even demand curves, both from residential BEV usage and industrial strategies for cost optimization.
The pessimist's case for a non-renewable economy are just hopeless at this point. All of this stuff exists now, is competitive now, and will only be getting better. It will take time to build out, but the economics are impossible to ignore.
There are a quite a few industrial processes which have energy as their primary cost. Aluminum is one example.
If a region needs 10GW average, one could build a wind installation with 10GW average output and a lot of storage to match supply and load.
Or one could build a 100GW installation, a little bit of storage and an aluminum smelter. During normal operation the smelter gets 90GW and the region gets 10GW. During peak operation the smelter gets a lot more than 90GW. During a trough the region gets 10GW and the smelter gets nothing. You'd still need storage or a peaker to handle periods when there is absolutely no wind or low wind and high demand, but those needs would be much less.
I don't know if aluminum can operate with such fluctuating power, but there are processes that can. At worst, bitcoin.