Edit because I forgot to mention this, if coal or ccgt were regulated like nuclear is, not a single one would be profitable. And even if you take into account every single death due to radiation poisoning (from any source) nuclear would still be the safest power source in the world. Literally worker deaths from installing wind power plants exceed it.
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.