If the power plants would shut down or be severely damaged, wouldn't the resultant lack of power cause all sorts of damage, including things like accident victi

If the power plants would shut down or be severely damaged, wouldn't the resultant lack of power cause all sorts of damage, including things like accident victims not being able to reach emergency services and all the other classic ripple failures? I can imagine there wouldn't be any direct casualties in the plant, but I can't imagine power plants that upon unplanned shutdown would not cause severe damage, including physical harm and death (albeit indirectly). Even power disruptions of a few hours cause deaths.