The Air Force backed the effort to build the Superbomb, as did the Armed Forces Special Weapons Project and the Joint Chiefs of Staff—although its chairman, General Omar Bradley, acknowledged that the weapon’s greatest benefit was most likely “psychological.”
Here's the thing about a Superbomb -- you need your threat to be plausible enough that you need to research how to make one, and how to make it look like you have one, but you don't really need to have one.
The threat is enough.
Of course, if you do have one, you want to tell the world, so they don't back you into a corner where you actually have to use the damned thing.