The only nuclear plant under construction in the US is at Plant Vogtle, in Georgia. Regulators set up a system (CWIP) whereby the companies building the plant earn a 10% return on their costs, until the plants come online. I think it's not surprising therefore that costs keep increasing and the delays keep coming. I don't think we can infer that nuclear power plants cannot be built at reasonable cost, rather that we need to consider "regulatory capture" as a significant construction risk.
(Some admittedly one-sided background on CWIP: https://stopcwip.com/ )