First off, the characters in the cutscene are merely a representation of the players in 1.0. There's four of them to represent a light party. Technically if rarity of the Job was an issue than the Warrior shouldn't be there either as they were also almost all wiped out.

The "real" reason is because Ishgard did not participate in the Battle of Cartenaeu. They declined helping the Grand Alliance in favor of protecting their own lands. The Azure Dragoon(probably Estinien at that point) or any Dragoon would not have been allowed to join the party. It's the only explanation that makes sense with the least plot holes.