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.
This argument assumes we must build nuclear power.
The problem is that electricity is fundamentally priced on the margin. Now that we are moving beyond a purely centralized design.
Think about a homeowner or factory with their own renewables and storage.
They fundamentally operate on marginal price by choosing when they use their own system and when they buy from the grid.
If you add state owned reliable power to this mix they will cherry-pick. Their own cheap electricity when it delivers and the states subsidized reliable electricity when it doesn’t.
We can try add all manner of markets, fixed connection costs and what not to this but all it does is introduce strange arbitrage possibilities in the market.
Which is why we have settled on net energy markets and then the lowest possible amount of ancillary markets to shore up any gaps which would cause problems for the larger society.
We have needed to build nuclear power since the day it was invented. The amount of fossil fueled power generation is indisputable proof of that.
The only way we don't need nuclear power is if we have some other way of producing the energy we need without dooming the planet, and obviously we do not as we're still burning billions of tons of coal every year. Not to mention gas.
We could have made power generation fully fossil free many decades ago if we actually took climate change seriously. It would have been fine. Sure fossil fuels may have been cheaper, but if you include the damage they're already causing and will cause in the future you could multiply the cost of nuclear by orders of magnitude and it would still come out on top. Plus higher investment would lead to faster improvement in the technology, mass production of components and lower cost etc.
I agree that renewable with storage is cheaper of you price in destruction of habitable zones of the planet. Most people don't, and the dollar cost of the storage is a problem over fossil.
This is also true of geothermal, which, like nuclear, is almost all fixed capital cost.