Not to speak for Diogenes, but I don’t think that there is a “right” to The Bomb, anymore than there is a “right” to have main battle tanks, battleships, submarines, or bombers. However, the question is more as to whether any of these consist of legitimate instruments with which to execute the (nearly universally agreed upon) “right” to national defense or whether they constitute such radically destabilizing or threatening influences that the US has the “right” to stop, by whatever means necessary, any attempts to acquire them in the name of our own defence.
I can’t imagine the other two members of the Axis of Eevil would not redouble efforts to gain what is apparently the sole means (barring unconditional surrender) of deterring US intervention after witnessing the demise of their erstwhile axial buddy.
That said, I think letting Iran (or anyone, pretty much) get the bomb is destabilizing and bad for us in general, for all the reasons that have been discussed above.