That's true of current nuclear, but it's not an intrinsic property of nuclear power. Proposed plants that use molten salt as a working fluid, for example, give you the option to run the plant all the time, but at any given time either use the heat in the molten salt for power generation immediately, or move the molten salt into a storage tank for later use. Molten salt is already used this way in concentrated solar plants, and works fine for that purpose.