Your proposal is to use nuclear as only backup? Or for only late nights (after batteries have discharged)? That dooms nukes economically, they need to run and sell power at close to 100% 24/7 to have any chance paying back the capex & opex.

What you’re saying makes sense but only for a planned state economy where the government owns (or subsidizes) all generation. It’s not possible in a free market economy, the nukes would go bankrupt/ never be built