Re: Reminds me of China
the 2/3rds figure doesn't rely on some heavy averaging - it is an aggregate figure demonstrating that the available energy from distributed solar is more than a token effort. I made no claim that the generation and demand were synchronised, nor that sufficient storage was available.
Lithium (and Sodium) batteries are a short term (~daily) storage, and give very rapid response times to keep the grid balanced. Flow batteries have the capacity for long duration operation with low storage costs, I don't know where Iron Air batteries sit in the scheme of things.
Pumped Hydro is slower, but more long term (weekly to potentially seasonal) storage - but it does have disadvantages in terms of space and specific geographical requirements.
There are other technologies around - indeed this is one of the potentially viable use cases for synthetic fuels like green hydrogen or air to hydrocarbon conversions, but there are also high temperature thermal stores being tested and I'm sure other technologies I'm not familiar with.
Dunkelflaute do happen, but in northern Europe they rarely last more than 24 hours (Li et al 2021) - with ~50-100 hours in the months of November through January - and more importantly the correlation between countries is relatively low (see fig 7 in Li's paper), meaning that connections between the grids in Europe go a long way to reducing the frequency and duration of these events.
But let's assume for a moment that we have no storage that lasts more than a couple of hours... that means that for 5-10% of the year we need to have additional generation - so for 90-95% of the year we get very cheap generation, and then we pay a little more during those short periods - don't let the "but sometimes" prevent taking up the solution that works the vast majority of the time, and provides a much lower overall cost even when the expensive periods are factored in.
Nuclear generally has the issue that it is relatively slow to react to demand changes, though modular reactors can, and should, be faster. They'll still need substantial storage systems though. Unfortunately the regulatory environment for nuclear power is hindered by the weapons potential of said facilities - and that is just one reason that wind and solar are substantially cheaper than nuclear power. I'm sure that with development of modular reactors the cost will drop, but the cost of wind and solar is nearly an order of magnitude below that of nuclear (Lazard, Oct 2020) so there is long way to go.
There is a good chance that some of the deep drilling geothermal research could yield a further source of reliable power which whilst not strictly renewable is sufficiently abundant that it may as well be.
The advent of many more connected storage device (whether thermal or electrical storage) also means that we can shape demand, and we can do to an extent that was unthinkable only a decade or so ago.
Is there a "single solution to all the problems"? No - but there are solutions, which when brought together can wean us off fossil fuels, and can do so with today's technology.
One important part of the solution that we shouldn't forget is that we should also be scaling down the amount of energy we use... that's going to be partly through efficiency gains (e.g. heat pumps rather than boilers, EVs rather than ICE vehicles), but partly through actually reducing the amount of energy (e.g. better insulated homes, reduced driving miles).
tl;dr:
Is nuclear part of the solution? Yes - it probably is. It's also got some really nice characteristics that fit in well with some of the newer demands being placed on the grid.
Is it the whole solution? No - because there is no "one" solution.