Blue Mage already has mandatory skills that it acquires through its job quests, like other jobs. The bulk of its skills also deal burst damage similar to Black Mage. A core part of its rotation is restoring its own mana through Blood Drain, similar to how Black Mages restore their mana using Blizzard spells. Spells obtained from slaying the Chimera in Cutter's Cry also combo with each other, and there is another combo that can be used when an enemy is inflicted with petrification. Once a Blue Mage has skills such as these, it can combo magic and deal damage in a variety of ways.

It is a highly useful job, but I wouldn't go so far to call it game breaking because restoring its mana does take a while when you consider the high mana cost of spells like White Wind and Bad Breath and the low potency of Blood Drain. Also if bosses are already immune to stun in most cases, I don't think it could be that difficult to make future bosses immune to some of Blue Mage's status effects.