Nuclear plants don't deal with peak energy use either. For the peak, you need a plant that can quickly regulate it's power output up and down to respond to demand. Nuclear plants only work for base load.

There are nuclear power plants capable of throttling up and down at will. Not all designs work like that but some do.

Really? Are you talking about a tiny fraction of operating plants?

I think it's pretty common. I'm not an expert but I think most of France's grid is run that way. Wikipedia has a few details:

https://en.wikipedia.org/wiki/Load_following_power_plant#Nuc...