The Phaser bank shouldn't have had the swirly effect. It didn't fire a Phaser beam. It fired something else (some sort of pulse).
I recall in the dialogue, O'Brien manages to push some power through the phaser bank, effectively creating a phaser blast. Presumably he burnt out the phaser bank doing so, as he could only get one, though later said he might be able to get another. Obviously it was to all intents and purposes a phaser blast, as Jassad was supposed to think the station was armed. It looked like a phaser, sounded like a phaser, and the Cardassians read it as a phaser, so it was indeed a phaser.
More like the Bajoran provisional government would have fallen, and the new power-brokers would share Kira's views and send Starfleet on their way.Half of Starfleet probably hoped that Bajor would fall back in Cardassian hands, so that this useless backwater surrounded by hostiles would not cause further problems for the UFP.