It would be relatively easy to incorporate it into the class/job quests. Of course, that would bypass the mechanic of going out by yourself to find monsters to learn abilities from, but I can see it working as some sort of "hey, Blue Magic student, I found a monster that has a worthwhile ability for you to learn, it should be holed up in such and such region". At first, of course, the teacher would have to go with you to teach you how to learn these abilities, but later she would send you out on your own.

Maybe the way to make it unique would be to have the leveling process only teach a few basic abilities, and then loads and loads of job quests could give you the rest. That might require you start at level 1 though, because you wouldn't want a level 30 character starting with just three abilities.