Each dollar spent on a nuke is exactly that dollar not spent on renewables, instead. But it takes with it another dollar spent on coal while waiting for construction to complete.
The amount spent just on coal and coal plant operation during those ten long years is enough, by itself, to build enough renewables to displace the nuke. The cost of building the nuke itself is enough to build several times enough to displace the nuke, beyond.
And the renewables would come on immediately, displacing carbon immediately.
Without radically increasing build-out of renewables, we will fail to avert climate catastrophe. The exact mode of civilization collapse in that case is debatable, but global thermonuclear war punctuates many.