Per Ember Energy reports, a cost optimal new build grid is between 90% - 97% solar/wind/battery, and between 3% to 10% gas peaker depending on how much sun/wind your locale gets.
But you can't replace the gas peaker with 3% or 10% nuclear because in essence that gas peaker is supplying 100% of the power 3% to 10% of the time.
So you'd have to build nuclear plants that can supply 100% of the power. But once you have that you might as well use nuclear power 100% of the time because the rest is irrelevant. But that's about as far from cost-optimal as you can get.
As you mentioned, using batteries for seasonal storage is madness. So to get to 100% carbon free you have at least 2 other options:
1. use a different form of seasonal storage. China is experimenting with this. In 2026 they will double the world's pumped hydro storage capacity. But doubling isn't a lot -- the world doesn't have much pumped hydro. But it does mean they might start doing it at China scale in a few years.
2. Overbuild to avoid the need for seasonal storage. Solar works on cloudy days and in the winter. It just doesn't work very well. So you need a lot of it. Which is expensive, but still a heck of a lot cheaper than batteries for seasonal storage.
In reality, most places will probably say that 95% or 99% carbon reduction is good enough and keep their backup natural gas generators around for the occasional dankelflaute.
every single one of Ember's analyses are based on historical situations. That is certainly useful, and serves to demonstrate an important point - that wind and solar make economic sense.
There is not a single analysis out there that tackles the twin problems of meeting growing electricity demand with a power source that depends on an uncertain and changing climate.
You say "occasional" dunkelflaute, but we have no idea whether occasional is once a season or once a decade.
This is exactly where nuclear shines, because although it is expensive, it insulates a country against the vagaries of external forces. Whether or not that guarantee is worth the price tag is the question a lot of governments are grappling with and they mostly seem to agree that the value is indeed worth the cost.