It would take far more work than a one liner to make any sense for most of the class quests to refer to you as your job from the onset, as in most cases you're either special, a one of a kind, or in MNK's case, literally pioneering the art.
"Ah yes, before we'll recognise you as a heretical Black Mage which so much as even admitting you'd be interested in trying to learn the art, if you even could find the locked away tomes or someone who could read them would land you in a gaol, please study thaumaturgy for a little bit, we'll ready your black robes, pointed hat and eyepatch for your graduation."
Few jobs would work without a radical shift as most like the MSQ build you up to be something when it comes to the job, like ARR takes your from adventurer to Warrior of Light, the classes take you from one of many to one of few or "the one" in some cases, most would have to be totally rewritten, it's a lot of work for something they've mostly made a non issue by simply never using the system anymore. Like others have pointed out, the only thing that really needs to be done is stopping people from entering the duty finder without their job stones, unless it's a premade. Otherwise they just stand as a lot of lore from the past and a glimpse into an older part of the game, but they do little else and don't really get in the way, so why wast the limited dev time on a non-issue?