Nuclear is currently about 10% of global electricity production. We could go all-nuclear, therefore, by going 10x on nuclear reactors (less in fact because there are renewables too but nvm).
There have been two major, critical nuclear energy incidents - Chernobyl and Fukushima. I'll count them both, though see caveat [1]. That's 2 incidents in 50 years. If we went all-nuclear and extrapolated, that'd be 20 incidents per 50 years, or 40 per century. UN estimates 4,000 deaths from Chernobyl (contentious but I'll stick with it). Wikipedia quotes Fukushima as 2,000 deaths - well, 2,002 deaths caused by evacuations and 1 in the incident. Let's not mince around and make it 4,000 per pop.
40 incidents per century at 4,000 deaths per event, that's a total of 160,000 deaths per _century_. In return, we're basically carbon-neutral and don't need storage. How many people die if we're not carbon-neutral? Millions for a start. It seems like a no-brainer to me. Also subtract all the deaths from not-generating power using these now-replaced means, improvements to air quality from not burning stuff, and I think humanity is in a much, much happier place.
I'm not saying nuclear is without downsides, I'm saying if you take all the downsides on the chin, nuclearise through the nose, you're better off than the alternative of burning stuff. Solar and wind are great but plenty of regions would require months worth of storage, which we're nowhere near to technologically.
So, now some nuance:
[1] Chernobyl, as I understand it, was basically man-made. Fukushima happened in one of the most extreme environments - east coast of Japan, one of the world's most seismically active regions. Also nuclear safety went ahead since then - these were both designs from 70s (!), we're 50 years away from the 70s.
[2] There are proliferation risks (though I still question whether they are as bad as global warming), but most of carbon emissions are from rich countries anyway (and we kinda equate rich with non-terrorist).
[3] Nuclear is expensive, but it is because it got much safer. We could, presumably, just take the old, less safe designs and build using those - and recreate all the above back-of-the-napkin maths. We could instead assume nuclear is indeed very expensive, but then we'd need to reduce the expected death toll numbers.
[4] Many regions can perhaps, indeed, do without nuclear and rely on solar, wind and hydro - great, good for you. Can you really do it without gas peaker plants or other "top ups"? Well if you can even nicer, but plenty of places cannot. But that's all good, that means we need less nuclear to achieve the same zero-carbon goal.