What if Support Role was Added to FFXIV?

[MistakeNot]

Would it make sense to add a fourth role to the Trinity of Tank, Healer and DPS to help create a better balance between all the job classes?

No, unfortunately not. They would have to redesign every single boss fight in the whole game.
FFXIV is designed very closely around the Tank/Healer/DPS trinity, with damage output as the central stat.