Or they could just add a Bahamut-egi animation near our characters when we perform Deathflare to at least give us an illusion that we are summoning it and it's the one performing the attack. You know, like NIN's new frog summon jutsu.

And just like Silver said, pet commands are very clunky. Just imagine missing the trance window just because the "Bahamut-egi" decides it's auto-attack is more important than Deathflare. It's a good concept, though, but not viable because of how the game's pet system works.