Nuclear doesn't make sense for that purpose because it'd have to quickly be able to spin up and down. Most reactor designs aren't really able to do it quickly in normal operations, and those that can can't do so in a way that makes any economic sense. They're financially outcompeted by their alternatives.
Storage is the solution, which we can build today in a viable way and is rapidly becoming cheaper and cheaper.
The financial case for nuclear today is shoddy at best. It's why no company wants to touch it with a ten-foot pole unless heavy government subsidies are involved. The case for nuclear in ten years is, given the continuous advancements in renewable energy costs and battery storage tech, almost certainly dead.
I mean, not really right? The government can still ask the webshop, that probably took your name and address. Or the PSP that facilitated the transaction, they likely know too. It's not like Visa/MasterCard/banks are the only parties that know it now, and the others are usually also beholden to laws that let government agencies query things.