Nuclear power plants are expensive for the same reason that rockets are expensive. They're mostly handcrafted structures. And relatively very few are built. Plus their principal components are usually not serially mass produced.
Currently, there are only 54 commercial nuclear reactors under construction world wide. Only two are under construction within the US. Eleven are under construction in China, seven in India, and Russia, South Korea, and the United Arab Emirates each have four under construction.
However, the US is scheduled to build nine new-- nuclear submarines.
The advent of small nuclear reactors that are being developed within the US and around the world should resolve the high capital cost problem of building nuclear reactors-- especially if most of the electricity produced from nuclear facilities is used to produce carbon neutral synthetic fuels through the electrolysis of water to produce hydrogen and the extraction of CO2 from the atmosphere to produce CO2.
Nuclear power produces about 20% of the electricity in the US and more than 50% of the carbon neutral electricity in the US. But existing nuclear sites in the US could easily produce at least 80% of the electricity if small reactors were gradually added to existing sites.
However, I believe that small remotely sited-- floating nuclear reactors-- used to produce renewable methanol (eMethanol) will finally end the world's dependence on fossil fuels. Methanol can be used to replace natural gas in natural gas electric power plants cheaply retrofitted to use methanol. Methanol can also be used in fuel cell automobiles and power plants. Methanol can also be converted into carbon neutral jet fuel and gasoline and dimethyl ether (a diesel fuel substitute). And methanol can power ships.
The seawater in the world's oceans contain about 4 billion tonnes of uranium which could be extracted and used to power human civilization on Earth pretty much as long as the Earth still has oceans. The source of this uranium is the ocean's natural interaction with the Earth's continental crust which contains more than 100 trillion tonnes of uranium.
There are currently more than 160 floating vessels powered by more than 200 nuclear reactors on the high seas. And such nuclear vessels have existed since the 1950s.