It's about roles, since we don't know exactly how thsoe 3 ability concepts will work we can only speculate.

What comes to mind when I think of Arcanist and it's two jobs is this.

Arcanist and Scholar will in a sense play the same way, both have pets which can change their elemental form which effects the abilities they can use. Where as Summoners can summon a unique entity however by calling upon this entity they would need to recall it and summon another entity if they wanted to change their roles.

Arcanist on the other hand will have carby which will be able to change it's roles on the fly however their roles wouldn't have the same punch as what Summoner's egi's could do.

With Scholar you have a faerie that can change it's forms, but it seems to be an aura based class, seeing as they confirmed that Healing over time ability would be given to them and they would be more of a regen based class. Also in the official page they hint that they will also be an enhancer class so it's possible that SCH's faerie's will work much like how Bard's worked in 1.0 where they will be able to toggle their aura effects but the more they toggle on the higher the Perpetual MP cost is.

in my mind, I'm hoping that the three abilities work as followed.

Carbuncle=No perpetual MP cost that can change it's form using MP or maybe even have it where the elemental forms work like the Pugilist elemental fist in 1.0 where there is a perpetual MP cost to them while in that magical state but the perk of Carbuncle would be the abillity to change roles on the fly

Summoner=uses Egi's for more defined roles but egi's would have a perp cost attached to them however instead of using MP to perform their attacks they would use a combo of either TP, MP or in some case MP/TP to perform their actions, forcing summoners to not only pay attention to the perp cost of keeping the summon out but also an eye on their TP to be sure that said Egi can perform the action at hand

Scholar=Faerie's will most likely be aura based, with each toggled aura increasing the perpetual cost of the faerie, and may have it where the longer the aura is up the more potent it becomes much like the XI ability "Avatar's Favor", which in XI lowered the perp cost of the avatar and provided players with a supportive AOE that became stronger the longer said avatar was kept out and as long as the ability remained active.

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So with that in mind the simple reason why Carbuncle has to stay on Arcanist is because it's roles are potentially interchangeable which is the opposite of how Summoner works. If Summoner's were given access to carbuncle it would give players little reason to play Arcanist since what makes Arcanist unique would no longer be there.