That's a fundamental problem with nuclear plants. Their classic "baseload" niche is gone. Like the intermittent sources, wind and solar, they need storage to hold what they overproduce during peak periods.
This is also true of geothermal, which, like nuclear, is almost all fixed capital cost.
It's only a problem because of capitalism. Every plant needs to independently make money, so nobody wants to be the ones spinning down because that's their profit margin dwindling.
But society would be better off with excess generation. So we either need a system where some are incentivized to spin down, perhaps by being paid a consistent amount regardless or something like that, or we need publicly owned power generation that doesn't care about profit.