Nuclear isn't an economically viable option for base load. Nuclear is the most expensive form of power generation. If there is excess supply, forcefully turning off renewables to buy electricity from nuclear would make the electricity needlessly expensive and kill the free market. In other words: it can only be a base load if we massively subsidize it and throw away free renewable electricity.

On the other hand, nuclear isn't a viable peaker plant option either. Virtually all of its costs come from paying back the construction loan, so a nuclear plant which operates at an average capacity of 10% will be 10x as expensive as one operating at 100% capacity. And 10x higher than the already-highest cost isn't exactly going to be competitive when battery storage, carbon capture, hydrogen storage, or even just building spare capacity are also available options.