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I'll resist the urge to spell out why and how you have particularly bad taste and instead explain that you're not exactly correct on the Eos/Selene being substantively different from Carbuncles to the point where there'd be any incompatibility.
Eos has 3 animations. Spell charging (Embrace, Whispering Dawn), Embrace Casting, and a third Twirling Casting animation used for the execution of Whispering Dawn, as well as the instant abilities Fey Illumination and Fey Caress.
Selene also uses those same 3 animations. Selene is, in effect, already herself a Pet Glamour, honestly even more so than our newly released Carbuncles are for Garuda, Titan, and Ifrit.
Emerald Carbuncle has 4 animations. Spell charging curl-up (Gust, Downburst), Spell casting uncurl (Gust, Downburst), Shining Emerald's unique animation, and a "scratch behind the ears with hind legs" animation used in Backdraft.
Not relevant to SCH but worth mentioning, Topaz Carbuncle has 4 animations unique to it. Gouge makes up its Malee attack by way of a somersaulting tackle, Shining Topaz is a standing spin attack, Curl is a unique standing self-buff animation, and Storm is a slightly different variation on Gouge.
As you can pretty plainly see, Emerald Carbuncle clearly has enough animations already existing to be able to take the place of Eos or Selene, especially since those two are in fact pretty barebones as animations go.
I would however like to take a moment to address the outright silly comment you chose to close your post with, as it's a baffling mentality I've seen echoed about a fair bit in response to the likes of Egi and Egi Glamour.
The Egi Glamour system is no more "just admitting the egis were a disappointment to begin with" as the Clothing Glamour system is "just admitting that everything you wear in the game is ugly except the things I or you like." Egi Glamour is a thoughtful response to the fact that, had they introduced new Egis without some system to encourage Summon Rotation (that is to say, rotating between different summons during battle), we'd be in the exact same position we found ourselves in without additional summons. You know it, I know it, everybody knows it. For just about anything you do right now, Garuda-Egi is the go-to Summon for the job. A new summon without a reason to use multiple summons in a single encounter would only accomplish one of two things. It would either replace Garuda-Egi as the one-and-only Summon, or it would be markedly worse than Garuda-Egi and not see common use until a buff comes along and changes our situation to the one where it replaces Garuda-Egi. Even you must admit that neither of those are desirable outcomes.
Additionally, limiting 'new' Summons strictly to future expansions adding a Summon IV, Summon V, etc kind of sets a hard limit on what summons we could ever feasibly acquire. Like, at that point we'd be lucky to get anything beyond Leviathan, Ramuh, Shiva, and possibly but very unlikely a Bahamut or Odin.
Instead, a much more sustainable long-term idea was proposed. An idea to reduce summons to individual roles and leave their appearance up to the player. Yes, implementation of Egi Glamour has been extremely slow (taking until the penultimate patch of the expansion to make good on their promise) AND only starting with a pretty sparse offering (not even an Obsidian or Diamond Carbuncle, despite bothalready being perfectly present within the game), but I think it's a step in the correct direction. What this means is, in the future, we can potentially receive Egi corresponding to just about any Primal we encounter. And really, having been a SMN enthusiast prior to Heavensward, the idea of being able to pick and choose which Summons I use is more than I could have asked for.
Now the only long shot is whether or not we'll ever be graced with the majesty of a Remora-egi.