There's a very dark scenario where for some reason or another (all out nuclear war or asteroid hit) sunlight is blocked, in which case having stable base load energy production from nuclear would be very useful. I know this is an unlikely scenario and hopefully it never happens, but it's always good to think about tail risks like these.
The world doesn't even have the foresight of doing something basic, like mitigating against fuel crisis scenario, let alone what you have suggested.
Volcanic winters are far more frequent than catastrophic asteroid blasts. Disregarding a volcanic winter possibility and its impact is like disregarding the possibility of a pandemic.
Surely you must realize that the fuel for nuclear power plants is not more freely available than sunlight. In the event of "all out nuclear war or asteroid hit", you're not getting those shipments from Kazakhstan.
If sunlight is blocked the amount of people who die due to starvation from crop failures will probably more than make up for the difference in lost solar power energy. That is to say, we'll have much larger issues than a stable power grid to contend with.