I want to write some points, why nuclear probably will not play any significant role going forward:
- In 1000 tonnes of uranium ore, there is 1 tonne of uranium. This contains about 0,7% U-235 used as fuel in most civilian applications. U-235 is used in the fuel in concentrations of about 3-5%. In the end, from a tonne of uranium, you can make about 100 kg of fuel used by a nuclear reactor. This is all used up in about a day in a largish installation. So you have to dig and process 1000 tonnes of ore each day to keep a 1 GW electrical output reactor running. The recycling of the fuel isn't economical unless you have a nuclear military program or want to do some research with various isotopes. That doesn't seem like a huge improvement compared to coal, gas and oil. Nuclear just isn't very clean in this respect either.
- The technology and mentality of how we build actual nuclear reactors is stuck at best in the 1980s. This might change, but there isn't any conceptually new reactor running in production anywhere. Compared to wind and solar, where replacement with better technology is the norm, this is just nuts. Also, wind and solar starts to be competitive to fossil fuels when producing electricity in some cases.
- Solar and wind don't have to produce stable output if the output is very cheap. In such a case, it will be economical to build better transmission lines, motivate consumers to adjust use based on production capacity and finally invest in clever energy storage projects. Good transmission lines (which we will need anyway, because of EVs and other electricity consumers) will spread out the production and load in such a way that the Central Limit Theorem will guarantee something similar to the traditional "base load" https://en.wikipedia.org/wiki/Central_limit_theorem Cheap batteries acting basically as grid capacitors will smooth out most of the peaks in production or demand, which will make the whole thing more economical still. (As we can already see in several places.)
- For winters, long term energy storage from the summer or very good inter-continental transmission lines are needed. This is not a solved problem but we still have plenty of time to think about solutions, but we really should think about them. Just building something conceptually stuck in the 1980s that is more expensive just to ensure we have electricity and perhaps heat in the winter without having to think about perhaps more efficient solutions doesn't seem like a situation we want to be in. We can decommission existing power plants over the next 10-20 years, while we think about storing the energy/ producing energy intensive stuff mostly in the summer or something like that. There is e.g. the possibility to produce ammonia, sodium metal or something else with excess energy that we can transform into electricity in the winter. There is also HVDC lines that might actually connect continents, which would solve some of this as well. There really is plenty of energy in wind, solar, tides/ waves, etc. that we can use. If it is produced at a low enough price, we might be able to throw some even rather substantial portion of useful energy away to transport it to the consumers be it on a different continent and still end up with cheaper power.
It might be more economical to buy storage to have enough for the winter or to transport some form of fuel. I think, the reality will be a mix of all approaches.
- We might do a better job of insulating our homes and more stuff like that to reduce some obviously inefficient use of electricity (e.g. for "just" heating, cooling, drying). Actually making infrastructure better is a good long term investment as it enables new approaches to solving problems and makes the quality of living better for everybody but especially for the less affluent.
- Nuclear is regulated as hell, where wind and solar isn't really all that much. Wind and solar is very flexible, as can be seen in poor bu sunny countries, where solar is a way to have electricity most of the time without having to worry about diesel (or uranium for that matter). Some people have a much better quality of living thanks to the dropping price of solar electricity in their circumstances and they don't have to ask anybody for permission to use solar. They just throw it on the roof of a hut and have enough electricity to power a phone and a battery so they have light at night. They can now communicate e.g. about the price of their produce and educate themselves. These people will not see nuclear or fossil fuels as a solution when they progress into the middle class, where they actually can affect some things e.g. by engineering infrastructure solutions.
- Nuclear always has the risk of a nuclear meltdown, which just isn't an option in large population centres. We humans are just too error prone to be able to reliably design and handle this. Because we are quite risk averse and have all the preventive measures (that have failed multiple times already) the cost of producing nuclear power just skyrockets.
- Finally, if there were no nuclear reactors, it would be even more uneconomical to keep a large stockpile of nuclear weapons or to power attack submarines and other stuff that is made only for the purpose to solve problems by force. Perhaps there is some advantage to the fear of guaranteed destruction but in reality, we just wage wars using ransomware and proxy countries - nuclear weapons aren't useful there at all.
The other uses of nuclear science e.g. in scientific instruments, medicine etc. can be done without nuclear being used to produce electrical power. We will have the current reactors for perhaps at least two more decades, so we have time to think about this even without building any new nuclear power generating capacity.