I don't think nuclear's problem is safety. If it was cheap it would be built anyway. Do you think most people think the thick, black plumes of smoke coming out of a coal plant are safe? No, but at the time coal was cheap power and we build a lot of coal plants.
- It has historically been associated with nuclear weaponry, giving it an unsafe imago. Chernobyl and related incidents didn't help, and remediation of nuclear incidents is much more difficult than something like the aftermath of a coal pile fire.
- It was not really cheaper than fossil fuels for much of its life, and it is not cheaper than renewables now.
- Not many countries have the capability to build nuclear power plants, which means they need assistance from abroad. This creates unwanted dependencies. As a simple example, I bet Finland is not very happy about its Russian-built nuclear power plants right now.
- countries having nuclear not wanting developing countries to have nuclear energy that act as a gateway to developing nuclear weapons over time.(I think this was the case for iran, not sure)
- in case of conflicts/wars a nuclear site blowing up is a much bigger deal than a coal plant or wind farm blowing up.