Also why do you only mention solar and not wind? Maybe because eit would make your argument less convincing? The wind still blows at night, so you do not need battery storage to provide all the demand during the night.
Why are the same simplistic arguments being brought forward again and again. They have all been debunked.
Whereas with solar and wind, you need to do both, because you need the overprovisioned capacity to recharge the batteries.
But this is really a question of economics, the mix of how much storage you want to include is really a question of cost and the specific grid. One should also say that pretty much every grid already has some level of overprovisioning, because otherwise you run into problems when some exceptional events hit.
In the end why would you pay for more expensive nuclear if you can get more capacity for the same price with wind/solar. So it is cheaper to build the overprovisioning with that. Moreover if the current trends for storage prices continue then things become cheaper still.
Is it enough wind to meet all the demand at night? And what happens when it stops blowing as much as expected for a long period of time[0]? You still need baseline power generation for quite some time to come until those questions that, well, keep getting hand waved away are solved.
0: https://fortune.com/2021/09/16/the-u-k-went-all-in-on-wind-p...
The wind doesn't blow as strongly at night. It's much calmer.
Wind and solar are cheap now because their fuel cost is zero and the cost of grid reliability is borne by us - consumers. In a better world, the cost of balancing the grid at night should be borne by a solar PV generator because it caused the problem.
Even if you match the energy output of a solar and nuclear plant, the component of time is ignored. On a grid powered by solar, where will energy come from at night? How many batteries will you construct? The scale of these batteries is again something that’s dismissed by claims of continental-scale grids but has that been achieved anywhere? All the batteries in the world combined can power à giga watt scale grid for hours. That’s right, hours.
Nuclear is a solution in the here and now. It buys us time to sort through these problems while we work towards a better future.