Nuclear plants are massive, complex, tightly regulated capital projects. These require strong project management capacity. Most Western democracies have spent decades systematically outsourcing project management to various consultants (who are great for reducing cost on small projects with short timelines, but not good for major projects with a lot of schedule and budget uncertainty). Couple that with the fact that the US and France haven't built a nuclear plant in decades (France started two in the 1984-2007 gap), causing the loss of most institutional knowledge. I think these are the root cause of price and schedule escalations.
Same problems have caused cost and schedule escalations in the Site C dam and the Lower Churchill hydro project in Canada. High speed rail in California has similar issues. Similar causes have affected the Berlin airport, and the Stuttgart railway station reconstruction.