This is what I'd like to see too. The current Cycle where you go from DoT Phase -> Nuke Phase -> Pet Nuke Phase -> DoT phase -> Nuke + Pet nuke phase isn't really what the Job Fantasy is. A lot of that is the reminants of older Summoner designs that have been changed as the game has moved on, but that design debt is really holding back on the Job potential.
Going from Ifrit -> Shiva -> Bahamut -> Ramuh -> Leviathan -> Phoenix, with a bursty finisher between each phase is much closer to how I would imagine the Summoner playing in an MMO.
Sadly, I can't see them ever changing the job in this kind of way. The fact that they've integrated abilities you learn into the story means that any kind of Job overhaul can potentialy also mean a re-write for the job story too. There are also, no doubt, players who enjoy the Summoner in it's current form who would be very upset if things were changed this dramatically. It would go far beyond just a simple redesign.
It wouldn't even be like Machninst, where they kept most of the abilities and names, but changed how they functioned. It would be straight up replacing one job with an entirely different one that just happened to have the same name.