Nuclear power plants are ultimately not that different from coal power plants. Typical estimates for the capital costs of coal power are ~$4000/kW, which can be used as a lower bound for the costs of nuclear power.

The costs are high, because construction industry has suffered from poor productivity growth for decades. Renewables are getting cheaper, because they rely more on mass-produced stuff and less on hiring people to construct a big specialized building to house the power plant. Regulatory costs of nuclear power also largely come from poor quality control in construction industry. Regulators require something specific, subcontractors try doing that but often don't get it right, and regulators order them to tear it down and try again.