That consistent output isn't as useful as you think. Solar and wind are ridiculously cheap, so we would want to use them when they're available. That means winding down nuclear plants when those two spin up. I'm turn, that means those initial construction costs you mentioned aren't being efficiently ammortized over the entire life of the plant.

What we can do instead is take historical sun and wind data for a given region, calculate where the biggest trough will be, and then build enough storage capacity to cover it. Even better, aim for 95% coverage in the next few years, with the rest taken up by existing natural gas. There's some non-linear factors involved where getting to 100% is a lot harder than 95%.