A more correct analysis is that CDT defects against itself in iterated Prisoner's Dilemma, provided there is any finite bound to the number of iterations. So two CDTs in charge of nuclear weapons would reason "Hmm, the sun's going to go Red Giant at some point, and even if we escape that, there's still that Heat Death to worry about. Looks like an upper bound to me". And then they'd immediately nuke each other.

A CDT playing against a "RevengeBot" - if you nuke it, it nukes back with an all out strike - would never fire its weapons. But then the RevengeBot could just take out one city at a time, without fear of retaliation.

Since CDT was the "gold standard" of rationality developed during the time of the Cold War, I am somewhat puzzled why we're still here.