It's fun side content. And I think that's fine personally. Jobs they add as limited jobs are likely things they weren't going to add as normal jobs anyway.

You could make blu as a normal job, sure. But that would mean giving it a standard set rotation/toolkit and a job gauge and making it play by the same rules as every other job. It could be done. But I think it's good to have side content like limited jobs. Not everything has to be about the loot treadmill, I think having some things like this are good for the game.

It's true that blue mage, and characters obviously inspired by blue mage like Quina and Strago, have had varying ways of learning the spells. But it's also true that there's always been a collection aspect to it, whatever the method is. And as a normal job they'd be limited to leveling up and the occasional job quest. The LORE of the job could be tied to studying monsters and mimicing them but the actual collection aspect would be missing as a normal job.

Which could have worked. Every job, to varying degrees, is changed in FFXIV to fit into the mold. From minor things like black mages having different functions for fire/lightning/blizzard spells instead of them all being the same spell with different elemental attributes. To bigger changes like dark knight losing its hp sacrificing to focus tanking, or summoners having more persistent WoW style pets. (Though they've been trying to improve on this aspect the last couple expansions.)

But I think a big part of the appeal of blue mage would be lost if they fit it into that mold and lost the collection aspect. And for better or worse this isn't the kind of game where they're going to design a main job that's 'that' different from the others and require so much extra work to get its full toolkit available.