More generally, though nuclear faces considerable obstacles, among the most serious are designing a high-risk, high-complexity system for a very-long-term deployment. How long do you expect nuclear to be human's primary fuel source, and how do you plan to deal with non-technical challenges.
Modern technical society is about 200-250 years old -- most sources date the start of the Industrial Revolution to about 1800. Virtually all our present institutions, companies, science and understand, etc., have emerged or substantially evolved during this time (though of course many trace back further).
Running nuclear power at global scale from here until Doomsday means planning at the level of centuries, if not millennia or even millions of years. That's timescales exceeding the oldest people, companies, governments, schools, religions, languages, even basic systems of morality and ethics.
Provisioning global-scale nuclear power would require on the order of 15,000 plants operating simultaneously. Unavoidable metal embrittlement limits these to a practical life of about 40 years. That means commissioning and decommissioning plants at the rate of one per day, and both processes are themselves 20-40 year endeavours.
That occurring through political and economic crises, wars, natural disasters, political and moral revolutions, and more. Things which are somewhat difficult to engineer around.
Even trace amounts of some nuclear contaminants are exceptionally poisonous, and at the proposed scale of operation, risks of release are decidedly non-negligible. Present human experience is limited to about 400-500 reactor cores, and there have been at least 4 major core integrity breaches, including Chernobyl and Fukushima. Substantial fault in all accident cases devolves to human and management practices, again, exceptionaly difficult to engineer around. With 30 times that many reactors operating from now until Doomsday, what acceptible accident rate are you targeting? We're at about 1:50 reactor years. Are you going to bump that up 10 - 100 fold?
At 1 per 100 reactor-years, we're looking at 150 core meltdowns pere century. At 1:1000, 15. You'd need to exceed 1:10,000 to limit yourself to 1.5 failures per century, and again, that through political strife, economic crisis, mob and mafia involvement, corruption, war, and natural disaster. Forever.
Renewable energy systems based on solar, wind, geothermal, and hydroelectric sources have far more benign failure rates. And I say that despite the fact that the worst power plant disasters are included in that list. China's Banqiao Dam failed in 1975 (itself a story of engineering, design, management, communications, and meterological factors) killing 171,000. Despite that, the region is now home to over 7 million people. The long term effects of such failures is relatively minimal, compared to the nondiscretionary multi-century wildlife refuges now surrounding the former Chernobyl and Fukushima sites, as well as smaller-factor radiation problems at locations such as Hanford, Washington.
https://en.wikipedia.org/wiki/Banqiao_Dam
More generally, the problem I see is that which was the real core message of the 1972 book Limits to Growth. There are limts to growth, and at exponential scales, those are reached rapidly even with increasing resources or pollution-absorption capacities by powers of 2, or 10, or 100. Those limits need to be embraced.
Nuclear power is just one of numerous cases of pleading for exceptions from the Gods of Complexity. The real challenge (and one Gates also acknowledges, though generally privately) is of accepting the limits of humans' footprint on this little, and rare, and lonely planet of ours.