Even 1 hour of stability with a relatively short restart period (under 5 minutes) would be fine with a battery system assuming the rest of the power plant was c

Even 1 hour of stability with a relatively short restart period (under 5 minutes) would be fine with a battery system assuming the rest of the power plant was cheap enough to build and operate. Nuclear already gets taken offline for several weeks for refueling, but redundancy covers such issues.