Easily available in what context, though? To us in the modern day, yeah, it's probably pretty trivial to mine such nuclear fuels, but the article discusses a lack of that technology.
There is less fissile material than fossil fuels. And the reactors are huge and heavy. Thousands of year maybe at current consumption levels, not if all energy consumption was replaced with nuclear.
I am not sure what time spans you speak about. Thousands of years is possible on fission with current technology and at current levels of demand.