A couple of reasons:
- You'll need to manufacture terawatt hours of batteries anyway to replace all the internal combustion cars on the road, regardless of whether you charge those cars with nuclear electricity or renewable electricity.
- Nuclear power plants make for very expensive peak generating resources. They're only affordable for covering the minimum ("baseload") demand that is always there on the electrical grid.
Consider demand on California's CAISO grid. On a hot summer day like 2019-08-15 air conditioning pushes the peak demand over 44 gigawatts. On the same day, the early predawn load is 20 gigawatts lower at 24 gigawatts. And on a cool day like 2022-02-06, the minimum demand is down to 16 gigawatts while the whole day average is well below 23. You can use the date picker to look at "Demand trend" for different days here:
http://www.caiso.com/todaysoutlook/pages/index.html
Only ~16 gigawatts of generating output will definitely get consumed all the time, but you still need to plan for those hot days that need 44+ gigawatts. It's theoretically possible to build 45 GW of reactors and use the full capacity for just a few hours a year, but that's very expensive. It's much more economical to have only 16 GW of reactors and use other electricity sources to meet higher demand, but that's bad for the climate when "other sources" includes fossil fueled power plants like it currently does. Nuclear plus storage would be much more affordable than using 100% nuclear without storage, and it would be cleaner than using fossil fuel peakers.