Nuclear takes hours to days to respond to load change, so there has to be much more reactive power available. And nuclear plants need to be able to draw megawatts of power from the grid any time they're not generating power. You can't "cold boot" a nuclear power plant without a massive external power supply and it takes days to weeks to do so.
It's so bizarre hearing people advocating for nuclear talking about storage like it's some barely-understood, dangerous, hideously expensive sci-fi pipe dream. Grid-scale energy storage is almost 100 years old and battery based systems have been actively deployed for many years at all levels of the grid, right down to residential.