The other reason that nuclear can't compete with natural gas is that combustion turbines are just inherently cheaper than systems based on steam turbines.
Steam turbines requires at least two systems to transfer heat across solid/fluid boundaries. In a coal burning power plant, these are the boiler (where heat is transferred from the hot combustion gases to the water/steam) and the condenser (where waste heat is transferred from the low pressure steam to the cooling water). PWRs have three such boundaries (fuel rods, steam generator, condenser).
In constrast, simple cycle combustion turbines requires no transfer of energy across solid/fluid interfaces. Combined cycle plants do, but for only 1/3 of their output. As a result, the power density of a combustion turbine based power plant can be very high.