This is a fair point! Quina, I believe, was officially referred to as a Gourmand, and it wouldn't be unreasonable to say that Gourmand is a different job that happens to be able to use Blue Magic (referred to in-game as Blu Mag). Gourmand also has the Devour ability, which makes a reappearance in FFVIII as a GF skill bearers of Eden can (comically) use.
Khimari was not called a Blue Mage, but with the exception of Yuna the Summoner, NONE of the characters had job names, in spite of the fact that Lulu was clearly a Black Mage, Auron very much resembled a Samurai, Rikku could be classified as an Engineer, and so on. In fact, Khimari had several Dragoon traits as well, such as having Spear as a weapon and being able to Jump (though, Jump was one of his "Ronso Rage" Overdrive abilities, a category which includes all of his learned monster abilities). So he could be thought of as a Dragoon who could use Blue Magic, or a Blue Mage who can wield spears and jump.
I don't believe that FFVIII ever gave jobs to their characters, and Quistis is therefore never explicitly referred to as a Blue Mage - but at least in her case, her Limit Break was actually called Blue Magic.
Regardless of whether they were explicitly Blue Mages, fans of the job type tend to enjoy the above characters just the same, as they like to collect all the different spells. I would guess that's a big reason why a lot of the Blue Mage enthusiasts in this thread chafe at the idea of Blue Mage in FFXIV. The level of hand-holding and refusal to allow players to be excluded from content for building their character "wrong" means that the likelihood of a learning mechanic that requires a player to go out and collect spells is slim. Like all jobs, the Blue Mage job in FFXIV would very likely have a character acquire every ability as a matter of course just by progressing through their job quests. There goes the collect-them-all charm!
They COULD change things up, since Blue Mage is a special case - but this is one point Yoshi P was clear on, that he was afraid a Blue Mage player would be excluded from content because they had not acquired particular spells.