Cutting to the chase: what is the biggest problem with the current Summoner? The rotation is boring. Why? Because the player doesn't have to think about the rotation! Theoretically, the new Summoner should be a job whose rotation is based on decision making over complexity, but the options available don't make that much of a difference so that the player wants to make a decision. The difference between choosing Garuda over Titan is almost negligible. For decisions to make sense, they need to be both punitive and rewarding. But of course this is not the only problem. Here's how I'd fix Summoner:
Aetherflow Mastery
Trait
Upgrades Physic to Whisperwind and Resurrection to Aurablast.
Whisperwind
Abilty
Cast Time: Instant
Recast Time: 1s
Mana Cost: -
Range: 25y
Area: -
Deals unaspected damage with a potency of 200 and restores HP equal to the damage dealt.
Aetherflow Gauge Cost: 1
Aurablast
Ability
Cast Time: Instant
Recast Time: 1s
Mana Cost: -
Range: 25y
Area: 5y
Deals unaspected damage with a potency of 100 to the target and all enemies nearby and restores HP equal to the damage dealt.
Aetherflow Gauge Cost: 1
What this does is take away two abilities that Summoners shouldn't have and replace them with something useful. Also, it gives purpose to a meaningless mechanic such as Aetherflow. Now Summoners have the choice to spend Aetherflow charges with Fester and deal more damage, or save Aetherflow charges to use Whisperwind in case they take damage. And before you say that Summoners don't heal (I'm looking at you, Yoshi-P), I'll ask you to play FFIII/FFIV/FFV/FVI again.
Summon Ifrit II
Additional Effect 2: Decreases damage taken and movement speed by 15%.
Duration: 20s
Summon Titan II
Additional Effect 2: Increases damage dealt and damage taken by 15%.
Duration: 20s
Summon Garuda II
Additional Effect 2: Increases movement speed and decreases damage dealt by 15%.
Duration: 20s
Now, instead of randomly choosing summons, the player will have to be constantly aware of the situation he's in, because he won't want to be on Titan when he takes damage, he won't want to be on Garuda during a dps check, and he won't want to be on Ifrit when he'll have to move around. The player, however, will be rewarded for his situational awareness, and this alone can make the rotation much more dynamic and fun.
QoL Sfuff:
For the love of God, make Carbuncle be permanently active and change Summon Carbuncle to Place. All the other Pet Actions are useless (instead of maybe Heel) and I can't even use a hotkey to move my fricking rabbit. If you don't want to add abilities based on Carbuncle positions fine, but at least leave me of the burden of having to summon Carbuncle whenever I die.
And lastly, the Summoner's questline sucks ass. I could write a story ten times better but this is a topic for another post.