While your points are well-taken, apparently the POUTUS is the only person that can authorize a nuclear strike and there is no one else in the command chain that can countermand that order once its given.

The rational for this goes back to the Cold War where there was at the most only 40 minutes between the detection of a Russian ICBM launch and the nuke detonating on its target, there was simply no time for second-guessing the President.