You do that and solar power isn't cheaper than nuclear any more. Also, for almost any storage technology you can think of to add to solar it can be added to nuclear too. This is especially true with high temperature reactors that get as hot as any solar thermal system. Nuclear power can heat up that salt too, and do it all day and night, meaning less mass of salt needed since the reactor runs as base load all the time and the sun shines only a few hours in the day. When it comes to reactor down time the utilities figured this out already, they put three or four reactors on a single site so that for scheduled and unscheduled shutdowns there is a high probability of power staying up.
Storage doesn't make solar power look better, it makes it look worse.