The short answer
Nuclear weapons are maximally anachronistic for 1844. That is the point.
The longer answer
Satire about institutional secrecy works best when the hidden object is obviously impossible. If the Files claimed Joseph Smith had a better printing press, a secret map, or a suppressed revelation, readers would pattern-match onto real historiographical debates and the deadpan would curdle into something meaner — or worse, into actual conspiracy content.
A nuclear device in Nauvoo cannot be mistaken for a live claim by any reader who finishes a page. The form of the archive (citations, probability weights, careful non-claims) can still do its work. The payload cannot be laundered into belief.
Adjacent choices we rejected
- Aliens. Too crowded; the register would collapse into existing UFO discourse.
- Time travel. Too genre; readers would expect plot.
- A conventional explosive. Too plausible; the satire would become an accusation.
Nukes stay.