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The main problem with nuclear power is that it's the most expensive form of electricity. People who say otherwise are only looking at the cost of running the generator, rather than including all the true costs involved in generating each watt, which is called the "Levelized Cost Of Electricity" (LCOE)
https://en.wikipedia.org/wiki/Levelized_cost_of_electricity
So there's no reason to build any new nuclear generators now that renewables+storage are the cheapest form of electricity, and are also the easiest and fastest to build.
The problem is that LCOE is an imperfect metrics that does not take into account storage properly for grid with high percentage of renewables (that requires significantly more battery storage than current 4h window considered in LCOE). LCOE also does not account completely for time effects associated with matching electricity production to demand. There is no clear metric for this, given that the cost depends on the structure of the grid itself and is specific for each country, but the Wikipedia article you posted show in the graph a very incorrect picture. Renewable (solar and wind) + storage is in the $80–150/MWh range, while nuclear is $130–200+/MWh range. It is worth noticing that nuclear cost is very high in Europe and US but can be actually very cheap (reason why china, the world leader on renewable is also world leader on new power plants). Estimation for new Chinese nuclear is at $62/MWh (https://www.renewable-ei.org/en/activities/column/REupdate/20240927.php)
All measures are imperfect, that doesn't mean it's totally meaningless and should be disregarded. And it also seems like you're referencing outdated data, as the cost of battery storage seriously decreased in 2025. But by any measure i can find, nuclear is significantly more expensive than renewables+storage. Regarding China, their data is generally not trustworthy on any topic, but yes I'm sure nuclear can cost a lot less there than elsewhere when you can steamroll over the citizens that would be effected by a powerplant's construction, operation, and waste storage.
I'm not an expert in this at all, but I believe that private capital isn't investing their own money in new nuclear construction, and that tells the whole story about the cost per watt of nuclear. If nuclear was cheaper per watt after all costs were considered then private capital would be building new nuclear, but they aren't, so that means it clearly isn't.
EDIT
I just looked at your link and it pretty clearly says the opposite of everything you said. Quote from the intro of your article:
And
I know nuclear is expensive, but power generation isn't the only reason to build nuclear reactors. Nuclear power plants basically prop up nuclear science. Without nuclear power plants, you're hampering the chances of discovering a breakthrough that could lead to cheaper nuclear energy. And you're pushing back the timeline on fusion.
Also, medical isotopes used for cancer treatments are created in nuclear reactors.
This doesn't seem like a good argument. More research into renewable and storage technology can also lead to interesting discoveries useful in other fields.