The energy demand is not flat, it has peaks. If you don't flatten these peaks with storage, you need to build a production system that should be able to generate enough energy during the peak, but then, some of the generators will have to be turned off the rest of the time.
To illustrate the idea, let me invent some numbers: with storage, you have, let's say, 10 power plants to build that are running relatively all the time, producing an integrated total of electricity of, let's say, 100. So, if you paid X$ for building the 10 power plants, you will have X/100 per unit of electricity. Without storage, you may end up with, let's say, 15 power plants, but some are turned off 90% of the time. At the end, you also produce an integrated total of electricity of 100 (the integral is the same, the time of consumption is just shifted to create peaks). The cost of build is now 1.5X, and you will have to 1.5X/100 per unit of electricity.
On top of that, turning on and off a nuclear plant is less efficient than producing continuously, so the price of electricity increase even more.
So, even with nuclear, storage needs to be built. Once the storage is built, it means that the problem of intermittence of renewable is way less problematic.