It's a large amount of money, but the plants have a long service life. And once a nuclear plant is built, it's operational costs are much lower than other forms of electricity generation.

Simply saying "use PV plus batteries" really does not engage with the scale of storage required. The US uses 12,000 GWh of electricity per day. The world uses 60,000 GWh of electricity per day. Annual global battery production is around 1,500 GWh, and only ~300 GWh of that production is used for grid storage.

Even just provisioning enough batteries to satisfy the requirements for diurnal fluctuations of solar is far beyond the scale of what battery production can provide. Let alone fluctuations due to weather and seasonal output changes.