My 2 cents...
I thought Mother Giselle was a candidate as well, especially after she was with the "faithful" disciples in Haven and marched with them, led them in song, etc. Also, the fact that she was close friends with Divine Justinia (as per hinterlands letter). I really thought that was where they were going.
But instead, I think she was mostly there to show decency in the chantry...you know, that they are not all zeolots or power hungry, etc. Even her feelings towards Tevinters, shown through her Dorian dialouge, gives her a bit of humanity. She is not perfect, she knows it, but she tries. Hell, Giselle and the cute chantry sister in DAO that inserts food in the Chant really are some of the bright spots in the whole chnatry world, in my opinion.
But I think politically, the chantry does not choose the Divine based on who is most devout, or who is even the "best" at being religious (if that means anything). They had to choose someone with real clout, someone who could be feared and respected and who could invoke awe in her followers. Vivienne makes good points about this. The Divine is an icon more than anything. Devout women like Giselle need to be in the trenches, talking to the common man and making connections. The sunburst throne is a hugley powerful position, and needs someone who can be ruthless, I think. Someone who can think geopolitically. Thus, about 2/3 in the game, I realized that although Giselle seemed to be who was going to end up there, she just wasn't suitable for a position like that. So I was personally relived when I realized she wasn't even in the running.
Also, I wonder if folks were surprised that Quizzie wasn't in the races. I was...I mean, she/he is the herald of andraste after all...
Also, I love that it is called the "Sunburst throne". Sounds so...regal to me!