Days? Seriously? You know that is not true, don't you? The French nuclear power plants are an existence proof of that.
Nuclear does need to be supplemented with something else with low construction/fixed costs for handling the rare, extreme peaks. That will most often be some sort of gas-powered plants. This has nothing to do with nuclear powers "inability" to "respond to load change" and everything to do with the cost of building enough nuclear power capacity that will almost never be used.
On the other hand, we are still very, very far from being able to do really large-scale battery storage. We don't have the manufacturing capacity for the enormous number of battery cells needed and even if we did, the cost would be prohibitive. This will of course change for the better in the future but that is how things are for now.
I believe the French facilities have the capacity of doing load following, but are not doing it because it is less efficient (and therefore more expensive). So I would also not say "days", but it is also true that one cannot directly take a situation where nuclear has, so far, being used only for base load and pretend that load following will work exactly the same way.
I'm not sure why you say "rare, extreme peaks": the current demand is non-flat every day, with a difference between the trough and peak that is typically ~50% of the peak.
I agree that large scale battery storage is challenging. Maybe the solution would be to have some storage and some "wasted efficiency" by using nuclear plants in load following and turning them in stand-by every day during off-peak hours.
[0] https://www.rte-france.com/en/eco2mix/power-generation-energ...
Just getting that to an hour means a three order of magnitude change in the amount of connected grid storage. Good luck finding that much pumped hydro! The easy spots are taken already!
An hour is not enough, of course. That might handle some small variations in wind only. Of course, one diurnal solar cycle means you need to store power for 8-12 hours. That is another order of magnitude. So in order to do this, we need to increase our battery capacity by four orders of magnitude. Multiple days? Weeks?
Now consider that the demand curve will become even more extreme, as climate change increases demand for electric heating and cooling. And consider that you will also need to account for electrifying the cars on the road (because building out storage like this is a multiple decades project), which will place additional capacity demands on the grid.
The thing with storage is not that it's difficult, it's that it's big. Like the scale is you need to nationalize your extraction industries and turn your economy into a wartime economy whose singular purpose is producing batteries big. It's not a Tesla or Google or even a DOE scale problem.
I also don't understand your argument about solar cycle: solar is producing close to peak hours, while nights are non-peak hours. So, in practice, it's not like you need to store the electricity locally for more than a couple of hours. I guess you are talking of a situation where the grid is 100% solar, but that's obviously a ridiculous scenario that no one has never pushed for.
I agree with the fact that the demand curve will become more extreme, and it is exactly the reason of my intervention here: this is a complicated situation, and it does not matter if the grid is mainly nuclear or mainly renewable, it is still problematic.
I agree that the storage problem is tricky and that the scale is a challenge. But this challenge still exist in full nuclear grid, unless we end up with a lot of idle nuclear plant running only few hours per day.
Nuclear takes hours to days to respond to load change, so there has to be much more reactive power available. And nuclear plants need to be able to draw megawatts of power from the grid any time they're not generating power. You can't "cold boot" a nuclear power plant without a massive external power supply and it takes days to weeks to do so.
It's so bizarre hearing people advocating for nuclear talking about storage like it's some barely-understood, dangerous, hideously expensive sci-fi pipe dream. Grid-scale energy storage is almost 100 years old and battery based systems have been actively deployed for many years at all levels of the grid, right down to residential.