The core problem is that there's simply nothing for a summoner and their summons to do in this game, as it currently stands.

There's no MP management, so there's no need to choose between summons based on how you're trying to draw down your MP for the duration of the fight. There's no real concept of aspected damage, so there's no need to choose between Ifrit and Shiva based on elemental weaknesses, or to avoid Titan if all the enemies are flying. There's only limited room to make cast times a thing when SE seems hellbent on designing encounters that force you to move around constantly.

Whatever model of summoning you choose (I personally think of Rydia over Yuna), I'm not seeing how you make summons appreciably different from each other, except for in visual effects. And that's the real tragedy.