I think it comes down to a fundamental misunderstanding of what a summoner is and does. Summoners don't have pets, they don't do most of the damage themselves with a pet to supplement, that would be more of a Beastmaster or Puppetmaster.
Summons are their partners, where they do heavy lifting and you support them and fight vicariously through them. They are your weapon and shield both. They are not your pets.

Almost every other game in the franchise gets this right. Esp FF11, where you went on an epic quest for each and everyone of your summons, where they felt like part of your family by the time you were done.