Since the job's icon is literally categorized as a DPS caster, it seems like Blue Mage should have AOE attacks for Limit Break at the very least; it's weird to me that it's the only combat class or job where I can't use that button at all.

One possibility for the future is that it could become a high-level trait rather than a spell or role action, where the effect of the Limit Break is based on your mimicked role; that's what I would personally to see, although I'll be happy with just anything in the meantime.