This would be correct if not for the fact there already is a core blu rotation for damage dealing, as over half the spells blu can learn are straight up copies of each other, or inferior versions of each other. The 220 potency aoe meme exists for a reason
Edit: For the unitiated.
16 220 potency skills, with the only standouts being Rams Voice for freeze, Electrogenesis for range, and sharpened knife for weaving. No axing required, you could take any of these and be doing the same amount of damage.
17 <220 potency skills, mostly situational/useless. Standouts are Bad Breath for the damage down, Sonic Boom as a ranged weaving tool, and honourable mention to Black/White knights tour however it only half works because most dungeon mobs are immune to bind so it only reaches half its potential, and it doesnt work on bosses. Honourable mention as well to perpetual ray for stun locking in full blu parties in certain scenarios, scenarios which cannot occur if blu was a full job. No axing required, however most of these skills are already not used due to being too situational or downright bad.
5 damage buff skills. These would come under mandatory in a full job scenario. Pec Light/Off Guard, bristle and moon flute would all be mandatory, whistle would be more dubious due to if they would allow final sting. Again no Axing required
3 kill yourself moves. Doubt these would be allowed if blu was a full job, remvoing them doesnt remove identity however imo.
9 Pure utility moves. All of these are already never taken over damage or more useful skills, so could already reasonably be considered axed outside of memeing around/ carnival (these are moves like snort/ loom/ sticky toungue ect)
Primal Skills: One of each cooldown length is already mandatory. Would involve no axing as you could take shock strike or mountain buster and be doing the same damage.
Magic Hammer/Devour/ Song of Torment. Again already considered mandatory, no axing required
10 Defensive Utility: The most controversial set of abilities. Stuff like white wind or exuviate would see situational use in the raiding scene and have that "clutch" factor that could save a dungeon run. Mighty Guard and Diamondback however would only ever see limited use as a way to try and solo tank some fights, however as most fights can already be solo healed, yet is attempted by very few people I wouldn't see this as too much trouble. These are the ones I could reasonably see getting Axed or limited in group play but I still do not think that axing some of these would lose BLU's identity.
5 % skills. These would again need axed or heavily adjusted to work in party play. Some say these skills are a part of BLU's identity, in that case adjusting could be in order for them. They already do not work on raid bosses themselves, only adds, so if adds gained immunity, and if the success rate of level 5 death was toned down so it doesn't demolish an entire add pack if you're a little lucky then they honestly wouldnt be too powerful, (level 5 being 25% chance per mob on a 5+ min cd wouldn't be too powerful given how pulls are gated, launcher already can't be spammed due to mp cost and the other % moves are single target)
and Finally Condensed Libra and Aetheric Mimicry as "blu only" skills. These skills only work within the context of BLU only parties so would either be useless or just straight up axed in group play (mimicry giving you permanant devilment is not adding to blu's identity)
In summary, the majority of BLU's skills would not get the axe in a full blu setting due to how similar/useless they are. The few that would be axed I would argue do not add to blu's identity in such a way that we wouldn't be blue mages without them, and the ones that would be adjusted to remain would also be still in line with being a blue mage.
This is all not even mentioning that the entire concept of being a "Legitimate Blue Mage" is an abitrary construct to begin with, and as various other final fantasy games have shown can be as limited as learning less than 15 skills, or games where they do not learn any "problem skills" only having damage and support.
Edit 2: My counting might be wrong but the point still stands