That’s what got Fukushima btw - when they shut the reactor down and then the backup generators got destroyed, they lost their ability to pump water to cool the reactor (which requires significant electrical power), which proceeded to start to melt down the core, and causing massive hydrogen buildup, eventually blowing up the reactor building.
Some new designs allow more effective emergency passive cooling, but the issue remains - nuclear plants are great for baseline power, but they aren’t good for sub-day, hourly, or finer grained peaks. Both economically and technically. Think ‘fully loaded container ship’ or ‘multi-mile long train’.
Pumped storage, battery, or fossil fueled turbines are great for those faster reactions - and often can provide useful sub-second grid stability too. Think ‘speed boat’ or ‘passenger car’.