I could see Blue Mage being added with the current combat formula in mind. DPs, Tank, Healer, filling one of those roles. The idea of being a Professor of Monsters isn't mutually exclusive as others have said. The idea of it being a job-specific hunt log/sightseeing log is quite appealing to be honest. Blue Mage enabling an in-game bestiary would be fantastic. Seeing something unique like that for other jobs would likewise be pretty interesting. I'd love if Black Mages could gather information about different kinds of Voidsent. Or if Paladin was able to fight various, 'Champions,' of Eorzea, building a bit of background on characters, such as the Company of Heroes.

Obviously you can't really do something like that with every job, but I think it would still be a fascinating addition to the game and really help make the Jobs have more flavor and individuality from one another.