I see your point about WoW, but in that game a character's job was part of their identity. You would make a priest, and that's it - they would be a priest. Wearing warlock gear would potentially go against that character's entire way of life. In FFXIV, you're encouraged to dabble in many professions. It's not only allowed, it's expected, and you are rewarded with recognition for it - even if I do a quest on my WHM, if it involves the CRP trainers they might remark on how I'm an old friend to the guild. So following on from that, it's a strange inconsistency that I'm allowed to walk around chatting to the DRG trainers as a WHM, wearing The Azure Dragoon as my title, yet for some highly specific reason I can't equip the DRG armour I worked hard to obtain in an in-character lore-heavy questline unless I grab my lance first. It breaks my immersion, frankly. It makes some level of sense that you need the right weapon in your hand to pull off certain moves and fight - nobody's going to be performing DRG lunges successfully with a frying pan - but clothes are clothes. Especially when you earn them in a quest and you're not even trying to wear the actual clothes themselves, just a replica projected by a glamour prism based on something already in your character's wardrobe.
I think it's fair to expect the person glamouring the 'cross-class' item to have to be able to equip it already on the same character when they have the appropriate weapon equipped, rather than a level 1 CUL suddenly being able to wear CUL AF in dungeons as a PLD. The effort of acquiring the additional looks should be part of the fun. But once they're earned, why not let the player themselves decide whether they want to project as a traditional knight or a jack of all trades or even a suspicious impersonator? The ability to instantly switch classes is one of the charms of FFXIV, and locking glamour seems to go against that feeling of freedom when shaping your character into a well-rounded, battle-hardened adventurer.