I have no idea where you got these numbers, but nuclear energy is good for base load, while batteries are good for handling load peaks. These two types of load are very different.

With big batteries, nuclear energy can be accumulated at night and used at evening, which improve performance of nuclear stations a lot. Try it yourself at simulation: https://www.tennet.eu/fileadmin/user_upload/Our_Key_Tasks/In...

Current cost of power storage is below $100 per kWh stored in the newest designs.

It's a near verbatim quote from the Cell article in the post above mine.

~ $300 - $700 /kWh.

that figure could be outdated but its in the ballpark

So nuclear is much much much much cheaper and until the storage costs come way down, we have no other choice (aside from natgas peakers). Correct?

For baseline power the answer is yes. The only two forms of low carbon baseline energy we currently have are nuclear and hydro.

Do you know why California is using batteries instead of cheaper nuclear? Is it just for cynical political reasons?

No one is using batteries at a large scale at this point.

User "jeffbee" said that California has 250MW of battery facilities right now

I assume that's 250MWh, and California consumes 260 TWh per year, so that's 30s of power consumption.

No, it's 250MW of peak power. I'm not sure what the total energy storage capacity is for California, but the typical project has 4 hours of capacity.

For an example please see this PG&E project which is coming online in Summer 2021. These installations have 700MW of power capacity and each has a 4-hour discharge time.

https://www.pge.com/tariffs/assets/pdf/adviceletter/ELEC_582...

You're right about the numbers, but still this is tiny at the scale of the grid. 2.8GWh is still only around 5 mins of consumption. You would probably need a few days of storage to run a 100% wind/solar grid, so that's about 1000x more.