The problem are week long wind droughts with heavy cloud cover. That's where there's a clear argument for geothermal, hydro, and hydrogen. Maybe natural gas with carbon sequestration. If nuclear wants to join these options, it needs to prove itself as something that can be built. And as somebody who doesn't believe that we are close at all to natural gas with carbon sequestration, I think we are a lot closer to making that work than we are to having the managerial and technical skill capacity to build new nuclear.
Nuclear is not the only option, we have so many more.
We have that with current generation systems too; we don't run natural gas at full bore all the time, usually. Most generators run at a capacity factor far below 100%.
The difference is that renewables generate power at zero marginal cost, while a natural gas turbine has fuel costs and wear and tear.
So we are going to have massive amounts of super cheap energy, for those applications that are not time sensitive.
Hydrogen production through electrolysis would be a great way to store this extra, nearly free energy. However this is unfortunately not a perfect match the intermittent surplus of renewables, since the capital costs of electrolyzers makes it so that constant production would be best. But at least some surplus energy will go this route.
Storage has several options, for example we could store hydrogen only for short periods before converting to methane or ammonia or other more stable chemical forms. We could convert pipelines perhaps.
Hydrogen has a lot of difficulties, but it is also, even now, an essential part of our economy and we work with it at scale. It will be a while before "green" hydrogen from electrolysis is cost competitive with fossil fuel derived hydrogen, but it will almost certainly happen.
There's a great, but long, two part series on hydrogen in Europe from what most would call a very skeptical stance, yet as a fellow hydrogen skeptic it convinced me that hydrogen will play a much larger role in the future:
https://about.bnef.com/blog/liebreich-separating-hype-from-h...
https://about.bnef.com/blog/liebreich-separating-hype-from-h...
And also industrial feedstock, immediately, and after a while, aircraft fuel.
While you can do an emergency shut-down quickly, normally adapting the power output of a nuclear plant takes many hours:
https://www.quora.com/How-long-does-it-take-to-shut-down-a-n...
The usual figures given for PWRs are something like "These reactors have the capability to regularly vary their output between 30–100% of rated power, to maneuver power up or down by 2–5%/minute" (https://en.wikipedia.org/wiki/Load_following_power_plant#Nuc...). This means that you can regulate your PWR over its power range within slightly more than half an hour at worst.
There is a lower limit to how much you can regulate your reactor down due to various limitations like Xenon poisoning. Because of that, a controlled complete shutdown is slower, because you need to get through the "icky" region between e.g. 30% and 0%. Also, you usually prepare for the longer phase the reactor will stay shut down. But all in all, shutdown is different from load following, and a conclusion that nuclear plants can't load-follow from a question about shutdown is just asking the wrong questions and drawing questionable conclusions from it.
It's not so easy when you have to meet it even when there is no wind or sunlight for twelve hours straight.
> In other words, you're running your nuclear at a 50% duty cycle, doubling it's price.
You're still running it at a 100% duty cycle, you're just shifting the generation times. You have a reactor that can produce heat enough to generate 1GW continuous power, so it stores that heat for six hours a day during peak solar generation, then generates 2GW for six hours to cover peak demand in the evening, then generates 1GW directly for twelve hours overnight. It's generating 1GW worth of heat at all times, you're just converting the heat to electricity at different times of the day.