"pets" nowaday are juste proxies for your actions that either :
-stay slightly behind you
-go to the target
-stay/go to a position and don't move
they may auto attack/heal.

That is pretty much exactly what the wyvern was in XI : following you, auto-attacking your target, and using a breath on certains actions you use.

Chocobo use actions on it's own and is still on the aggro list (like most pets prior to ShB) other than that, it has more control on it's behaviour ("role" mode) and it's actions are locked behind a grind system.

"worst" case (if anything get done) : idk if it's possible , but just glamour "blood/life of the dragon" ? just an option to replace the blue/red animation and have a wyvern instead ? (like carby/egi glam). that way it's not "more visual clutter" ; juste a trade