Plats survive some time (days) without light. If there is not enough backup power source (peaker gas plats, not nuclear though) the grid could quickly collapse causing a continent-wide blackout from what it would be really hard and it would take a long time to bring the grid up. Cities would be uninhabitable within a few days (no water, not sewage processing, no heating).
Not to be too simple about it, but this does happen every night. We already require (and achieve) sufficient grid diversification, without batteries and all the cool stuff coming in future.
I am not against nuclear, but I do believe we would be fine without it too.