Then what storage of some good few hundreds of megawatts would you build for a tiny fraction of the cost of a nuclear power plant, that also fits where a nuclear power plant could be built?
There are many alternatives to batteries, for longer term storage. Tanked anhydrous liquified ammonia may be common, particularly for smaller and more isolated utility districts, in part because tankage can be topped up from imports if it runs low.
Underground or sea-floor compressed air are practical, as is buoyancy, in many places. Many more places can use pumped hydro than have an existing dam, or watershed; either up a hill or down to an underground cavity.
The method used will be whatever is cheapest in the place and time constructed. Cost for most methods is falling fast.
Building a nuke is by far the most expensive baseline alternative, provided it can even be approved and built on a useful schedule.
Nant de Drance has 900MW of storage, and took 14 years to build. Each of the last generation reactors in Hanul generate 950+MW of power, and took 5 years to build. The first newer generation reactor is 1340MW, and (assuming it keeps its schedule) has taken 10 years to build. They've done the first tests so they have some chance of connecting to the grid this year, but let's be pessimistic and say that it will take another 4 years - matching the construction time for Nant de Drance.
That's still ~50% more power, and it is actually generating it: for Nant de Drance to help, it also needs >900MW of actual renewable power generation plants to be built and operated.
There is little economy of scale, in pumped hydro. California stores a much larger amount of energy in numerous reservoirs all over the Sierra Nevada range.
(The "synthetic baseload" comparison is favorable to nuclear, as dealing with variable demand can only help renewables as it already requires storage, and that storage can serve double duty in the variable demand case. Similarly dispatchable demand and transmission between countries also only helps renewables.)
It's difficult to get nuclear to compete with wind+solar+batteries+hydrogen in the 2030 cost scenarios. Nuclear does least worse in places like Poland then.