This, though. I've been thinking this for years. Leave Carbuncle as a full-time pet and autosummon him on job change, for those who would miss Carbuncle. Have him just be an extra always-on auto-attack. Replace him during Demi-summon phases as is already the case.
Then, make the summoner's spells poof Demi-primals into existence for one-off attacks. For example, upon becoming SMN,
- Replace Ruin with Call: Strike. Poofs a Demi-Primal into existence for a single strike.
- Replace Outburst with Call: Burst. Poofs a Demi-Primal into existence for an AoE attack.
- Replaced Bio with Call: Sap. Poofs a Demi-Primal into existence to inflict the target with a DoT.
- Etc.
Classically a "Call" spell should summon a random Demi-Primal from among those the player has defeated, but of course specific Demi-Primals could be assigned to specific actions. So basically, while your Carbuncle buddy is out slapping things with his tail, you're summoning a sequence of Demi-Primals who appear, do one attack, and then disappear. When you get to a Demi-Bahamut or Demi-Phoenix phase, Carbuncle is replaced with Demi-Bahamut or Demi-Phoenix, and as you continue to summon one-off Demi-Primals, your Demi-ElderPrimal contributes their attacks as well.
With no meaningful changes to the way SMN plays, this change would drastically realign them stylistically to the classical image of a Final Fantasy summoner.