You still hear people compare nuclear costs to coal because coal was competitive in the 1970s. They quit building coal plants at the same time they quit building nuclear plants, for the same reason —- gas turbine generators based on airplane engines have a capital cost about 10% of the steam turbines used for coal and nuclear.
Even if the heat were free and you could burn coal without asking “what do you do with the waste?” you would struggle to be profitable with either coal or nuclear…. Unless you could couple these energy sources to a gas turbine. In the case of coal you need to gasify it (say make hydrogen out of it and pump the carbon underground) in the case of nuclear you need a new reactor type that runs at higher temperatures (liquid metal, molten salt, gas cooled) and a breakthrough in closed-cycle power sets. If it succeeded though you could fit the power plant in the employee break room at the turbine house of today’s LWR.