

Huh? Modern nuclear power plants automatically stop the reaction. In addition to other safety features monitoring things like temperature, radiation, etc. for automatic shutoff, the rods are held in place via electromagnetism. In the event of a power loss, the reaction will stop because the rods fall out of place. (This may just be one type; other modern reactors have ways of automatically stopping the reaction in the event of a power loss.)
This exactly. You need a reliable source of fuel for the baseline, which is where nuclear energy can supplant fossil fuels instead of or in addition to relying on batteries.