Unfortunately nuclear doesn't appear to be a viable supplement.

Suppose a grid with just nuclear and solar. Nuclear may be overall very stable, but solar is still not, and so you still need storage. The only difference is how much of it you need.

But nuclear has a terrible problem: it's not really economical. Solar is much, much cheaper and therefore any economically minded person would build solar if they had a choice, and would just not enter the business space at all if they couldn't.

The business model of nuclear is just broken in modern times. The idea was that nuclear is cheap but unwieldy, and can be supplemented with small amounts of more flexible but more expensive sources for when it can't adjust fast enough. But that just hasn't panned out.