I don't think it is possible to remove egis, as that would require rewriting and remaking some of the SMN quests that involve or explain egis. If you change egis to temp summons, that means the 62+ quests that involve those SMN trainees and their egis would need to be redone to fit the new concept/mechanics.
Since I am a fan of redesigns when things don't quite fit and like to fantasize, I'll give some suggestions for a SMN design:
- Core of the design being SMN + Carbuncle: Carbuncle persists and acts as a source of supplemental damage and a way the SMN can protect themselves (for example, they'd get an ability to temporarily dismiss Carby to gain a substantial damage resistance buff, not unlike how SCH can dismiss the fairy to get a boost to healing output).
- Egis are connected to specific abilities: Much like the summons in the console FFs, egis appear only to perform a specific task and then vanish. Unlike the console FF summons, the abilities are not high-damage AoEs, but instead vary in effect and utility. For example, SMN might get a skill called Searing Wind that summons Ifrit-egi to cast it on a mob, applying a less powerful version of the mechanic from Ifrit EX (debuff that deals AoE damage over time). Likewise they might have an ability called Icebrand that summons Shiva-egi to deal frontal cone damage (unless we want to give SMN Icicle Impact with its vulnerability debuff). These skills could have their own separate cooldowns, or could share cooldowns depending on how they're tuned. They could also cost Aetherflow stacks if that is a better way to control their use. In this regard, SMN would function more like how Ultima Weapon uses primal abilities.
- Egi "abilities" could be upgrades to existing ACN/SMN skills: You could have something like Fester be replaced by Thunderspark (Ramuh-egi) after a certain point in the questline, which much like Fester gets a bonus on targets affected by Bio and Miasma and deals higher single-target damage. My approach would be 3 egi abilities as upgrades to existing ACN skills, and 3 egi abilities that are something brand new.
This would be designed in tandem with the trances currently in place, helping delineate the "tiers" in summoning. That said, it would take a colossal amount of work to make something like this happen.