I see the points everyone is making, and they are good ones.
In response to Tint directly: Absolutely Paladin and especially Dark Knight use magic in their jobs; and as I understand it, MP is even the Dark Knight's main currency instead of TP. But, I'm leaning more towards an esthetic mage class who is also a Tank. Paladins and Dark Knights still wield swords however, and what I would like to see is a Tank that is strictly a disciple of magic. The Psychic job could use headgear as their main weapon, equipping sick ass magitech to their heads in order to focus their telepathic powers. They shoot beams, could be more mobile than the other classes (with skills and techniques that mitigate its flaws), and put up walls - maybe they could have a literal ability to section off a portion of the field that enemies can't cross and negates all area of effect damage/statuses while inside it.
The Psychic class would be like a Tank version of an Arcanist. It hits with dots, AoEs, and super effective status ailments/debuffs. All the while giving out a passive aura of protection on people close to them, keeping allies from taking damage and avoiding decimating status effects or mechanics. It's Limit Break 3 could be like some time reversal: after it casts, it resets all team member's health, raises all fallen allies, resets everybody's timers like nothing happened, even reset the Limit Gauge so it can be immediately followed up by a second Limit Break (barring the Tank from executing it a second time). An almost meta-tier protection, where not even the games own mechanics and rules break through. Oh, the boss is casting it's special and we're all underprepared? Psychic job swoops in, breaks the game, and your entire party dodges the unavoidable, field-wide attack without a scratch.
This is the vision I have: Tank executes Limit Break 3... finishes casting... static quickly flickers over the screen, and it all goes dark for a second before "turning back on" and everybody is 100% okay.
On top of everything else, think of the story potential. Plot potential. Maybe we're introduced to the job by a team of Psychics who say they can travel dimensions. This is not unthinkable, given the lore of Eorzea. They say that while in this dimension, they want to recruit more people to go along with them. They teach you the basics of the job, then thrust you into a vortex that spits you out into another dimension (read: dungeon). What fun we could have with that! A Stargate in Eorzea with the power to travel dimensions using the aether. Lots of opportunities.
And like... yes, all of these functions could fall into the category of what a "Blue Mage" is. I'm not denying that. I'm trying to make the argument that Blue Mage might just be a little too close to heart (and close to Red Mages...) for fans of Final Fantasy. But here, in this obscure game that a lot of fans would outright say they don't like or have never cared to play, rises a mountain of new opportunities in the Psychic class. And if you think the two are similar enough that you might enjoy its play style if but under a different name, then why not give it a shot? And give newer or more ignorant fans of the series something fresh to play and fall in love with. And if the worst you can say about the job is "I wish it was a Blue Mage" then to that I say: mission accomplished, boys.