As a general observation I've noticed a very deliberate separation of the job quests from the rewarded abilities this time around. I don't believe any of the new job quests directly relate to the granted level 70 ability. Instead everything is handled as vague concepts of acquiring some sort of secret or new training.

Given the way many of the pre-50 job quests were gutted and no longer reward the skills they actively talk about I imagine the developers have decided to avoid that issue in future by not tying abilities directly into the lore like that. It's rather unfortunate though as many new skills feel rather out of place, such as Demi-Bahamut's existence now rendering the previous logic regarding failing to summon Ramuh-egi irrelevant.