You're a victim of a common misconception. Nuclear reactors can ramp up and down as quickly as the control rods move. Check out the Borax experiments (from shutdown to full power in seconds) and the TRIGA reactor (from shutdown to gigawatts and back to shutdown in milliseconds).

What can't ramp quickly is the steam turbine connected to the reactor, but that's more of a design decision than a technical limitation. The German nuclear plants ("Konvoi" series) can in fact ramp faster than the German gas turbine plants, because that was a design requirement.