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I used to be anti-nuclear energy until I learned a bunch of science and engineering behind it. Turns out things are less scary when you know more about them.
Edit: I also learned that it's okay, and usually preferable, to not have a strong opinion about things that you don't know about.
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)
I am unsure why you bring this up seeing as how nuclear power can not react due to load demand and instead only provides base load power, which means other power sources are required to keep up with transient demand.
Nuclear cannot manage fast transient, but for that we have gas peaker and batteries. But nuclear can indeed work in load following mode, with most modern nuclear power plant being able to reduce the amount of power significantly and circle during the day. The French fleet, for example is required to cycle between 20% and 100% twice a day, within 30 minutes. Modern reactors ramps up at 5% each minute.
That means that they can account for changes in demand. More data here: https://www.nice-future.org/docs/nicefuturelibraries/default-document-library/france.pdf