1) Adding more required skills that are required to progress the BLU-questline, to ensure everyone has a certain "standard"-kit, like every other job. Since other jobs just learn certain skills while leveling up and not needing their jobquest to learn everything, bluemages should get more skills from or for jobquests - either by them outright saying "In order to accept the next quest you need to reach level X and learn skills Y, Z and A" or by them just teaching you 2-3 new skills each quest.
2) Keep BLUs access to the DF limited until a certain point, maybe level 30, so the game has time to build up a proper toolkit for the job.
3) Make certain skills solo-play or arena-only - mostly things that instantly kill enemies (since they wouldnt/shouldnt work in duties anyways), that are to strong on the tank or healer front or skills that have a really low-learnrate, like the primal ones (this is to ensure that a bluemage wont get kicked because they dont have this certain rare spell)
3.1) As an alternative to my last point, to still keep the feeling of using such an epic spell: I like the idea of filling up a BLU-gauge and would propose that ones its filled up you can use one of those "special skills" - they would all be the same in terms of damage-output, but with different animations. Using the BLU-skill-menu you pick the one you like best and take with you into the fight. During the BLU-questline you should learn one of those skills for sure so you'll have access to this move but if you want you can farm the other ones for "show off".

I dont think that BLU would need a real rotation and could imagine it more working like bard - having several dots or debuffs you want to keep up and then single-target and AoE-skills.
I could see using a "skill-glamour"-system here aswell by giving the job certain skills that do pretty much the same (maybe with minor differences - 100 potency for 100MP for one skill and then 110potency for 150 MP for another one - just real slight variations that dont matter in the long run of a fight) and letting you pick the one you like best, either gameplay-wise or in terms of animation.
The quest will provide you with a "base-set", but you can get a slightly different ST-spell from another mob.
While I know about meta and usually speak out against customisation, because I dont really see it work in an envoriment where everyone just follows the meta anyways, I could see it work here given that:
a) the differences are mainly the animations, with only the slightes variation in skill-effect
and
b) your choices are being limited to pick one of the ST-skills, one AoE, one DoT etc. - instead of loading your hotbar with 3 STs and ignoring the rest.