No!  The Westinghouse AP-1000 reactors finally being completed at the Vogtle plant in Georgia are frequently cited as proof of this canard.  This project was first-of-a-kind, therefore bearing an enormous regulatory cost.  Westinghouse filed for bankruptcy during the construction, and the NRC made new demands after construction began which required demolition and redesign.  By contrast, the direct descendants of  this design are being built on budget and on time elsewhere in the world.  The South Koreans are building four in the United Arab Emirates, and several of the Chinese take-off are being constructed in China and elsewhere.  In fact the first AP1000’s are already operating in China.

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The economics change dramatically for the better when one design is selected and built out in multiples.  This is how France developed majority nuclear power at a reasonable cost in the course of one decade.

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Finally, modern Small Modular Reactors show the promise of much lower cost and much shorter build times which further reduces the cost of up-front capital.