First of all, Egis are an intrinsic part of SMN's identity, and have been from the very start (through lore/quests and supplemental material).
You would have a point there....if SE wasnt seemly stripping healers, and a few of the dps such as bard of their identity, as of current identity matters, but it seems to not be a focus for the team since whatever just gets melded into a class, wether it fits the tradittional role of that class or not (again, bard is a fine example of this)

What you propose would be akin to removing the cards from AST or the faeries from SCH.
So that's NOT changing.
No, what i propose would be akin to upgrading most/every summon from the dog sized Egis to Traditionally (like every other final fantasy game with a summoner) sized BIG BOI summons. adds far more form and function with every summon, not to mention looks.

Secondly, we already do have Trances/Demi-Summons for what you'd call "half-sized summons".
Hell, Firebird Trance/Demi-Phoenix already has an "exclusive" HoT buff when summoned, so there's that.
My trance plays a bit differently, its more of a "takeover" than a small phase, and your able to do it with any of the Summons rather than having it locked into a rotation with only 2 options...well, 1 if you consider its Bahamut trance first then pheonix in that order only.

And third (and most importantly), your "rework" would severely limit the amount of summons we would get
On the contrary my friend this would expand the amount of summons, as it could be any primal we have fought thus far (a lot), and no one said they couldnt be glamoured with a bit of thought into design

, as opposed to what the Egi glamour system could potentially give us (if they ever get around implementing more, that is)
.I wouldnt hold your breath on that one fam, its been years and we still dont even have a ramuh egi, not even a glam for it.