The lore of ARR states the Primals are the physical manifestations of elemental Aether (Ifrit = Fire Aether, Titan = Earth Aether, and so on) and the lore of the Summoner is that they can channel a portion of the Primals Aether to call forth the Egi.

So it really makes no sense where all these current abilities (Bio, Miasma) fall in place in terms of lore. These abilities are a contradiction to the Summoners discipline of channeling elemental Aether. It would make more sense to give the Summoner a series of elemental abilities that are dictated by which Egi is in play at any given time. So the Summoner essentially draws their personal abilities from the Egi in play. So if Ifrit is in play the Summoner would gain Fire based abilities, Titan earth based abilities, and Garuda wind based abilities. They could still be D.O.T based attacks of course just with that elemental overlay in order to give the Egi more of a focus and for the lore of the job to match up with the actual game play.