Overall mined uranium supplies are quite limited. Numbers back in 2013 [1] put the total uranium available (including estimated undiscovered resources) at enough to maintain current operations for 230 years. Bump up usage by an order of magnitude, and you're running out in 23 years. And Western countries (mostly Canada/Australia) only produce about 20% of that total.
So if nuclear ever became a staple, you'd end up needing to resort to salt-water extraction, or developing breeder reactors. Both would send costs skyrocketing. Salt-water extraction is also going to run into environmental issues given you're talking about processing literally trillions of tons of water (uranium's about 3 parts per billion in saltwater). Breeders also substantially up the stakes in terms of complexity and risk.
If you'd indulge my curiosity, what would be your opposition be to something like solar + artificial hydroelectric? It's relatively cheap, infinite (well subject to access to the materials necessary for construction of solar panels), completely safe in any scenario, and things like artificial hydroelectric take care of the biggest issue of day/night production.
[1] - https://www.scientificamerican.com/article/how-long-will-glo...