In France and Germany, nuclear reactors are configured and permitted to run in load following mode. It's harder on the valves and similar equipment, but it can and is done. 
> unless the renewables become incredibly overprovisioned.
Which is the likely outcome, as solar and wind are still declining in cost and in some places the cost is as low as 2 cents/kwh. The generation will be cheap (what's the old saying? "too cheap to meter"?), and it'll be the storage that'll cost a bit more.