How do do you think we harness the heat from a coal fired plant? We boil water! The steam turns a turbine and then the water is cooled in a tower and then expelled.
Nuclear replaces the first step, heating the water. The other steps are the same.
If you need guaranteed power at any time of day, fossil fuels and nuclear can provide that, solar and wind can't – while batteries can smooth over the intermittency, the amount of battery storage required to provide the same power availability as a coal or nuclear plant is cost-prohibitive. So, if we are comparing apples to apples, coal plants vs nuclear is a legitimate comparison, wind and solar aren't.
Pumped hydro does better than batteries, but building new dams causes massive ecological damage, and in some parts of the world fresh water is a rather scarce resource. The heated water from a nuclear power plant arguably does less environmental damage overall than a big new dam does.
Nuclear replaces the first step, heating the water. The other steps are the same.