Imagine US actions if in 2003, mushroom clouds would've actually risen over major US cities, out of a sudden. If you remember, Saddam did a last minute bluff, promising "fiery death" to NYC, and Washington, and this silly bluff did make not so few people in DC to turn pale.
Knowing how US politics goes, I would say US would've seriously considered rising a white flag, invariable how weak enemy's conventional forces are, in fear of additional strike.
Given that Israel would likely come under sanction due to non-proliferation policy, and the further pressure on Iran to develop their own, revealing the capability is problematic to say the least.
Hoping to keep it secret for some kind of strike like that goes right out the window once you've used it, and you will absolutely never strike hard enough to remove the nuclear capacity of somebody like the USA (that's why nuclear submarines exist).
The best nukes are the ones that never need to be used.
https://en.wikipedia.org/wiki/Dead_Hand
Surprise attacks with a super-weapon only works if you're the first to have one.
Again, that only works if you can "outpoker" your opponent, and if this alone will be sufficient to crush his will to fight back.
