It's doing much better in terms of actually being used as a large portion of countries electricity generation, as I demonstrated above. But more importantly, the reality is that nuclear isn't competing against renewables it's competing against a fossil fuel grid that's supplemented by renewables. Germany, the poster child for renewables, still emits 10x the carbon dioxide per watt of electricity as France.
Let me put it more bluntly. Renewables are indeed cheaper on a per-watt hour basis. But that's more than offset by the need to deal with intermittency. Batteries are great for cars, but they exist at nowhere near the scale required to decarbonize with a wind and solar generation base. More exotic proposals like thermal storage, hydrogen, or the Sabatier process remain in prototyping and academic stage. The cost of storage is a non-answer, because there's no real plan to build this storage.
Renewables make in a stopgap mitigation plan but we have no feasible way of building a grid that's powered completely or even mostly by renewables. If our plan is to decarbonize the energy sector, renewables do not offer a solution. Hydroelectricity, and geothermal power do, but those are geographically limited. Nuclear energy is the only source that can feasibly replace fossil fuels as a consistent, geographically independence, and carbon-free energy source.
TL;DR:
* Industrialization happened because we figured out we could heat water and push a piston (and later, spin a turbine). Modern society is built off the ability to produce mechanical and electrical energy from thermal energy.
* It's a lot easier to heat water and spin a turbine with a carbon-free source of heat, than to try and capture energy from sun and wind and store massive amounts of energy to overcome intermittency.