With batteries and thermal storage you can scale up over time. You can have a new small thermal storage or battery facility up and running in 2-3 years and slowly build it out over the next 20 years, with the option to change technology or capacity as needed during that time. With nuclear you have 20 years of 'nothing' before you have anything to show for your efforts.
It’s true you can start small and scale up, but it still would probably take many years to accumulate enough batteries to make a significant difference. Secondly, it doesn’t make 20 years to build a modern nuclear power plant, 5 years is a better estimate. So nuclear is still easily the cheaper/faster/proven method compared to batteries or thermal.
How I wish that where true. But looking at all current new Nuclear power plant projects in Europe and the US it's clear that we are incapable of that. Yes we can argue about why that is and how in theory it shouldn't take that long, but the truth is that best case scenario it will take you more than 5 years just to get a building permit to start buildings a new nuclear power plant.