I wouldn't mind if each eggi replaces the most of the SMN spells and provides a different "playstyle", with each eggi having a dps rotation befitting its role.

For example, on a single target fight you would summon Ifrit and instead of Ruin/Bio/Miasma/Energy Drain+Fester/etc., these all get replaced with Ifrit's melee skills, with a single target melee combo, a dot, and maybe a simplistic AOE combo. Then if you summon Garuda, you get ranged AOE comboes.

This shouldn't be that hard to balance because Ifrit could have terrible AOE potential (maybe on par with tanks) while Garuda could have terrible single target potential (again on par with tanks). Titan would have 0 damage potential. It would be the same as balancing any other DPS job because every DPS job would have to go through both single-target and AOE balance passes anyways.

From here on, there could be more eggis that would provide different rotations. For example the Ifrit rotation could be WAR-like, while another melee eggi would be NIN-like, another SAM-like, etc. The SMN can only "equip" 3 eggis at the same time.

The current iteration of the SMN doesn't really feel like a "pet job".