Here we go again...
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).
What you propose would be akin to removing the cards from AST or the faeries from SCH.
So that's NOT changing.
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.
And third (and most importantly), your "rework" would severely limit the amount of summons we would get, as opposed to what the Egi glamour system could potentially give us (if they ever get around implementing more, that is).
So all in all, I completely disagree with your "re-imagining".
EDIT:
Also, Seraph and Fenrir are not Primals.
And considering how SMN (the Allagan job) was conceived as an "anti-Primal" discipline (by using the Primals' powers/essences against them), it wouldn't be able to "summon" them at all.