Why didn't 4th Job AoE's get a cooldown?

No. Bishops do not have a built in advantage, aside from the meso cost. The advantage largely identified is circumstantial; Yes, Skele are weak to holy and nothing good is weak to Fire or Ice, but that's not an intrinsic property of Bishops. It's a flaw of the monster population, not a flaw of the class.

Bishops don't have a built in advantage? Where have you been? Mesos cost isn't the only advantage bishops have. It's getting into any party (boss run included) alot easier than a mage will. Bishops train faster than every class in the game INCLUDING mages.