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

I'm of the opinion that Bishop's required presence in boss fights justifies them getting better experience rates. If Bishops got poor experience, they'd be less likely to level, and they'd be harder to come by for bosses.

Agreed.

And while it's true Bishops are a huge part of bossing and required in at least one boss battle (Horntail), they have a much different role in bossing. They aren't attackers...at all. In large scale boss battles, their sole purpose is to support and keep the party alive. That's awesome - it's just not the role many people want to play in boss battles. If they didn't have their ultimates to make them a good class outside of bosses, too, their population would decrease. It's obvious how that would cause problems.