It can't cope with peaks. It has to generate the same power 24/7 to be anywhere near economical at two-three times the cost of solar+storage, so it either needs massive storage or massive overprovision
Lets say you have a peak demand of say 40GW but average demand of 600GWh a day (25GW), or 219TWh a year
Lets also say you have to shut down a plant for a week a year for maintenence
You need to build five, 10GW plants to meet your demand.
They provide 5 * 10GW * 24 hours * 7 days * 51 weeks or 428TWh.
If nuclear is $110 per MWh, that means it's going to cost you $47b a year to generate your power requirement, or $215 per MWh
So you're needing to roll out storage, same as you do for wind and solar, or spend twice as much on overproducing.