Jobs that are upgrades of classes don't have experience, and this sounds like a non-issue in my professional opinion.
Removing combat classes from the system does not necessitate removal of combat class quests from the system. Just change the quest icons for the 1-30 quests to the job quest icons, have NPCs refer to you as the class until you reach the job quests proper, and give everyone a quick bit of dialog at Lv1 that says something like,SE would have to scrap all the class quests, and have to make new 'from level 1' Job quests for the starting classes which just violates the lore in so many ways. It would just be too much of a can of worms for SE to bother with, with little overall benefit.
"Before the people of Eorzea can recognize you as a full-fledged [JOB], you must prove yourself a capable [CLASS]. The [JOB] job quests will become available once you have reached level 30 and completed the [CLASS] story line."