Let me put this into FFXI terms.

In FFXI you had the Job system. Jobs either specialized in a certain role or were jack-of-all-trades. JoaT's were shunned on because when you could have each person excel in one role, there was no need for JoaT outside lowman/solo situation. FFXI also had the subjob system but because most Jobs could excel in one role, the benefits of going cross-role were pretty negligible for balance reasons (you couldn't step on anyone's toes just by subbing a certain job). This didn't work all the time though as some Jobs received hefty benefits that arguably killed Job balance for some aspects of the game, like healing or tanking.

Now FFXIV's Job/Class system is different in the regard that when you do play as a Job (like in XI), you lose the ability to go cross-role but become more efficient in the one role you end up (and excel) with. On the other hand, once you play as a Class you no longer excel in one role and as the exchange for this loss in speciality you also gain improved cross-roleability (at least when compared to XI's). In a nutshell you become a JoaT for the situations that demand it while not giving up your performance in group situations where being most efficient at one role is preferred.

In FFXI to become a JoaT or excel in some field you were forced to level a new Job, or use subjob combinations that stepped on other Jobs' shoes (Utsusemi tanking for example). In FFXIV every player is provided with the opportunity to be a JoaT or a specialist, whichever the situation demands for. In exchange you either lose efficiency as a one-trick-pony or the ability to obtain the (negligible in balanced cases) cross-role bonuses.

I didn't edit my last post because a Yakuza threatened to kill me if I did. True story.