Revelations from Patch 2.55 [SPOILERS]

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And the whole story of "we don't have our weapon" is just assumption anyway.

Blatantly false. Pay attention to every cutscene that takes place in Ul'dah - YOU DON'T HAVE YOUR WEAPON.

If they rang the alarm bell, everyone in the city would know this.

Linkpearls exist. You know, that thing that Minfilia keeps bugging you with. They could sound the "alarm" and the smallfolk would be none the wiser. The Brass Blade rush would just look like some sort of incident happened in some other part of Ul'dah and they're moving to stop it.

the whole army can't just teleport in

Why would they need to when they're already outside the doors, everywhere in the city, ready to move at a moment's notice?

The Sultansworn are the Sultanas' guard.

Did you even read the PLD story dialogue? It's confirmed that a portion of the Sultansworn is paid off by Monetarist coin.