But even if nukes were somehow very cheap to build, the review process due to high safety requirements and a lack of a standardized reusable reactor design would make the process slow. To become cost-competitive, nuclear reactors need to be mass-produced, using a proven design that needs little review. The French sort of achieved that, with two mass-produced types of reactors.
Renewables as baseload are still problematic though. Solar cells and even wind turbines are not expensive, but the batteries are very expensive, and are a huge fire hazard. It would be interesting to estimate how much would a kWh cost from a nuclear power station, and from an equal-power LiFePO4 battery installation with the capacity of, say, 3 days worth of the rated max power. Batteries can be replaced gradually, but would need to be replaced much sooner.
[Update:]
If we take a modest nuclear generation unit producing 300 MW of electric power, I'd like to compare it with a battery that can store 300 MW * 3 days of energy from renewable sources. It's 21.6 GWh. With LiFePO4 typical bulk price of $100 per kWh, the upfront cost in batteries alone would be $2.16 billion. It's still lower than nuclear reactor equipment, but very much in the same ballpark.