Class specific, certainly, but Relic/Artifact was something very much more than class specific gear. Artifact armor sets had in-game story and history, but they also had a sort of meta-history in their connection to the previous FF games that made them that much cooler. With these entirely new classes there's no previous FF lore to base the sets on and so they will have to stand on their own. Conjurer Relic is probably out, but that doesn't mean you definitely won't find gear sets reminiscent of classic BLM gear and that of the other classic jobs. I still expect to find a purple helmet with wings, a distinctive red and white robe, and a floppy, brown steepled hat. Perhaps even a sweet red hat with a feather in it. A pimp hat, you might say.
And who's to say in a year there won't be upgraded jobs taken directly from the FF multiverse? Lancer can upgrade in to Dragoon. Pugilist can upgrade into Paladin. Marauder can upgrade into WAR/SAM/DRK. Conjurer gets WHM/BLM/RDM and Thaumaturge gets Time Mage and Geomancer, while Pugilist gets THF/MNK/NIN. This is SE we're talking about. They would do it just to watch the mayhem.
No, they're not really going to do that. The game is not set up for rigid job definitions.