I feel like the egis and carbuncles are the most visible part of summoner's identity. Taking that away and just having big-hit-then-gone summons would just make them black mages with books. That said, the base egis could use some help to make them feel less like filler. (Obligatory comment about egi glamours.)

Or maybe the demis could be diversified. For example, instead of all them going through Bahamut and Phoenix, give base egi a different demi evolution. So Ifrit would go from Bahamut to Zurvan; Garuda could go to Phoenix and Sophia; and Titan could go to Alexander and Sephirot. Spitballing here, but just an idea.