Job quests would obviously teach non-monster skills (BLUs don't just use monster skills only y'know)
As an Example (Cause let's face it, SE prolly isn't gonna do this)
Level 1: Learn (Learns a BLU spell from targeted enemy. Each monster has a base % of teaching the BLU their spell/ability. This % improves the lower HP the monster has. 0% at 100% HP, like 25-30% at critical)
Level whenever the first job quest is: Examine - 20-30 sec cast time but doubles the chance of learning a BLU spell on their next learning attempt.
Next ability could be like, Enrage. Mob focuses his learnable spell on the BLU increasing chance to learn said spell/ability by 10%. Before and after it uses the ability, it stays on tank (hehehe have fun learning tank busters). If used on the BLU that already knows said BLU magic, enemy potency heavily reduced.
Be the Monster: Next BLU magic cast has increased potency.

I think SE can make some non-monster skills to act as rewards for job quests. All other spells/abilities come from mobs.

There are lots of creative ways of making BLU work within the rule set XIV uses.