> Easily processed uranium will last us 80 years at current consumption rates. If you start building current nuclear reactor designs everywhere, we'll run out of it in less than 40 years.
This is a little pessimistic: these numbers rely on current proven reserves without reprocessing. Of course, if you want to use a bunch more uranium, prices will go up and the number of proven reserves will increase. This won't necessarily take a massive price swing-- heck, even at current prices new reserves will continue to be found.
> Then the price will skyrocket, and nuclear is already more expensive than renewables.
Fuel is a negligible portion of the cost of nuclear. You could triple the cost of fuel without materially impacting the operating costs of a reactor, and the overall costs of nuclear energy are not dominated by operating costs, but instead capital costs.
And, we're leaving out that reprocessing fuel is possible and proven (though there are proliferation concerns0.