[ben_w]

Nuclear plants can't be built instantly; the growth patterns for batteries suggest that by the time new nuclear comes online, there will be enough batteries.

(And I'm saying this as someone who actually likes nuclear, thinks the public perception of the danger is over-stated, and who thinks everyone should have build a lot more reactors decades ago).

[nithril]

Genuine question: would these batteries be always connected to the grid with enough power and capacity to feed the demand?

[ben_w]

Where the batteries end up and how they're used heavily depends on policy decisions between now and then.

I'm expecting most batteries (worldwide) to be used for cars, with bi-directional power so they can function that way (for grid storage) when plugged in. That doesn't say much about what any specific country will do, and as Texas demonstrates, US states can have their own independent energy policies.