This is nonsense the amount of uranium required is incredibly small compared to oil or coal. We are talking on the order of 1:100,000 or in the case of a proper breeder reactor even less.
Worse, this concern is making the usual mistake of only considering uranium. Thorium is a waste product from rare earth mining and is very abundant in the USA (and elsewhere). If we build thorium based reactors, fuel is practically unlimited and free (compared to the costs of running a reactor).
Uranium is fairly abundant AFAIK. Sourcing it is less of a problem than overcoming NIMBY.
Uranium available for enrichment is not fairly abundant. And U ore deposites are distributed far from fair. Like I said, China has no access to deposits, the UK secured for itself. Russia was effectively cut off Kazakh U resources, leaved with a _single_ mine in Chita region.
But this highlights what I think is the main problem with the large scale nuclear energy vision, it would replace oil with Uranium as the root of geopolitical resource control wars.