Likely because Governor Swann didn't want to be brought back from the dead
Davy Jones can offer mortals to serve him and postpone their death if they accept his deal.
Davy Jones: Do you not fear death?
Chaplain: I'll take my chances, Sir.
Davy Jones: To the depths.
Davy Jones: Life is cruel. Why should the afterlife be any different? I offer you a choice. Join my crew, and postpone the judgment. One hundred years before the mast. Will ye serve?
Helmsman: I - I will, serve.
Davy Jones: Grand.
Since Davy Jones powers come from Tia Dalma when she was Calypso, we can suppose that similar rules apply to her powers. So when she says:
Tia Dalma: Him at peace.
We can assume that she cannot (or maybe refuses to) bring back to life a soul that is ready for their final journey to the land of the dead, which seems to be Swann's case:
Governor Swann: I'm so proud of you, Elizabeth.
Governor Swann: I'll give your love to your mother.
Governor Swann seems to have accepted his fate, knowing that he will retrieve his lost wife, and that his daughter Elizabeth is strong enough to take care of herself. In opposite, Barbossa still had some unfinished business in the world of the living:
Barbossa: So tell me, what's become of my ship?