Nuclear plants are not good at rapidly changing to accommodate demand. Powering down a nuclear reactor is a big operation. Powering down a smaller reactor may be a smaller operation, but they still don't adapt as easily as gas turbines. Or batteries.

But the storage problem I was alluding to is the storage of nuclear waste. Some of it remains dangerous for an extremely long time, and storing it safely is far from trivial. There are several options, but they all have problems.

Similar to batteries for electricity storage, perhaps: there are millions of ways to store electrical energy. None of them are perfect, but on the other hand, they are improving rapidly.