It's not just about class names. Those are just flavor to add the 'FF feel' and potentially draw back in players that quit the game over a frustration of it being a generic MMO as opposed to FF.
The true draw of the 'advanced classes' is to specialize roles. So you can specialize in being a tank, a controller, a healer, a magic nuker, a ranged DD, a melee DD, a buffer... etc.
That is why we need to define playstyle. The class names are just a way to do it, and one that I think just about every FFXIV player present or future would be behind. Not to mention the history and lore behind something as simple as the name 'Red Mage' or 'Dragoon'.
If I need to explain without using past FF games, then the FF MMO could just as well be called Eorzean Adventures. Love it or hate it, the FF name brings in players who want to experience the FF mythos online.
Most chose (and will choose) the game to play a Final Fantasy, not to play a random MMO offering.