The problem with 100% solar+batteries is that you need to massively overbuild for the system to meet demand. It's far more cost-effective to have some portion of generation come from a firm, weather-independent source. The main options are fossil fuels, hydro, geothermal, and nuclear. Since fossil fuels emit carbon and hydro and geothermal are geographically limited, nuclear is the best option in a lot of places.
If solar becomes 2 times cheaper, it will be economical to capture nitrogen from atmosphere and produce ammonia and use that for long-term energy storage and fuel. And with that one does not need massive solar overbuild.
This does not require any magic technology, just scaling up what is available today is enough and will definitely happen within the next 20 years, before small nuclear will have any effect.
> firm
That's the opposite of what you want. You want something that is cost-effective to operate at a 10%, 1% or 0.1% duty cycle. Like nat gas or hydro. Not nuclear.
And overbuilding isn't the only lever you have to ensure coverage meets your target 99.99% level -- geographic diversity works really well (the wind is always blowing somewhere), and wind power production is usually negatively correlated with solar power production.