And even if you were able to keep building it, you will soon run into the storage problem which is still potentially more costly

I will tell you a secret: Nuclear power doesn't work without storage either. That's just something they will not tell you as that's their biggest pro-nuclear/anti-renewable argument.

Nuclear is expensive and running the amount necessary in winter is only viable because you have an overproduction most of the year to export. But when everyone runs either on nuclear, nuclear and renewables or renewables and storage, there is no demand most of year (as everyone is overproducing) and also nobody to import from in a few especially cold weeks in winter (so you need even more nuclear power you won't need most of the year). That's completely unaffordable unless you put in storage in place to cover some of your winter demand and export time-independent when there is demand in other countries (which is why French models for 2050+ plan with huge capacities of hydrogen production - not the most efficient way of storage, but good for export).

where it’s buildout may have to be many times more expensive to save power for months

Actually weeks. Wind and solar are quite complementary. So you only need to cover the rare circumstance of cloudy and windless... which doesn't happen more than may 3 weeks a year, barely more than a few days in a row (in a lot of countries even less if you geographically diversify).