There are many ways to store leftover capacity so that nuclear plants can operate all the time even when combined with renewable sources. For example, you could use leftover capacity to drive pumped storage plants. Pump storage plants operate at 70-87% efficiency [1] and can produce gigawatts of power on demand (in fact, within seconds). They are effectively the largest batteries in the world.
Other problems: you require a pretty significant hydrological infrastructure for PS: upper and catchment resevoirs, and a sufficient gradient to provide a net energy differential.
The logistics make multi-purpose use of PS systems (vs. typical flood-control or irrigation reservoirs) somewhat problematic as water levels may fluctuate dramatically over a brief period of time, and spillways/headways constitute a significant flash-flood drowning risk unless access-controlled.
Still, yes, pretty efficient energy storage systems overall.
[1] https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricit...