Nuclear has the same issue of intermittency. You have to either overprovisioning if you use nuclear or use battery storage. Nuclear is much more expensive than wind/solar so if you follow an overprovisioning strategy the best is to build wind/solar capacity, because it buys you more. Moreover, the larger and more integrated grids become (this is happening already for economic reasons in Europe) the less this is an issue.
Also why do you only mention solar and not wind? Maybe because eit would make your argument less convincing? The wind still blows at night, so you do not need battery storage to provide all the demand during the night.
Why are the same simplistic arguments being brought forward again and again. They have all been debunked.