1) No no, I mean the ability was originally Devotion. While not tied mechanically to Bahamut, it was thematically. The name and effect kind of implies a lesser or muted version of what Tempering would do. Though I guess one could argue it came from Ifrit...
2) Oh, it could be anything. But if it's too little, it would always be a loss. For example, 300 potency per gem would be a DPS loss unless you were using it to burn all three gems, as merely using one of the Primals already does 750 potency of damage for the same single GCD. So in a situation the boss was about to go untargetable and you had, say, Ifrit and Garuda up, it'd be better to hit EITHER Ifrit OR Garuda than it would be to use that attack. That attack would only be a gain if you had all three Primals up (900 potency for burning all three gems vs 750 for using any one of the Primals). So being that low would be pointless. It would have to be over 750 per gem to make it meaningful for one gem, and over 425 per gem to make it meaningful for two gems. And unless you expect over 55 seconds of downtime or the boss is about to die (in the latter case making it a button you only use once per encounter), you'd never use it on three gems.
2b) As for bloat, I recall once hearing someone complain about a grandma being a penny-pincher even though she didn't need to be because she was well off. But the thing is, she was well off BECAUSE she was a penny-pincher. How this applies here: If you don't concern yourself with button bloat when it isn't a major issue, it tends to become an issue. But in this case, it's more "meaningless" button. If the proposal was something really useful, I'd agree. But as discussed above, it's something that would probably only be used once or maybe twice per 10-14 minute fight. Is that REALLY worth a hotbar slot? I don't think it is. Though I do agree ED/ES and Fester/PF could probably be straight upgrades. Not as sure about Gemshine and Brilliance, but I suppose at that point there'd be no reason to still have a distinct AOE rotation. And I do think (saw your post in the Healer forum on Holy/Art of War, etc) that we've come to the point in FFXIV where having a separate AOE rotation is kind of pointless most of the time for most Jobs. So I'm not exactly against just rolling those into the single target rotation so they get more frequent use.
3) I'm more making a lore argument there than anything. Carbuncle has never been associated with much other than some very specific WHM (Time Mage in the case of Reflect under the Tactics Job system) party buffs. I do agree with Phoenix being kind of weird. They should honestly rework it as an oGCD (or GCD) that isn't tied to the main rotation that can be summoned as an independent effect. Like Curing Waltz on DNC isn't tied to the rotation, and it's because of that flexibility that it's actually somewhat useful. Phoenix isn't NOT useful, it's just useful in happenstance - when that part of your rotation happens to align with fight mechanics, but you're using it anyway regardless of the fight situation.
4) I get that. That's why I think it should be instant cast with the commands being oGCDs. Think about your own character. Hit Dia then Assize on WHM. Not hit Glare and then Assize. Note the difference. Hit Ruin 2 or Biolysis then Indominability on SCH. Now do the same thing with Glare. While instants can have a minor delay based on animation lock for characters, this may not be true of pets. But regardless, oGCDs come out as soon as the action is complete, which in the case of Instant cast Spells/Weaponskills is immediate. It may even be faster than a second oGCD following a first oGCD is, honestly (the latter imposes a ~0.7 sec animation lock). One of the things I like on SCH vs SMN is that Eos is always DOING something. She doesn't feel like a useless ornament. Sometimes her Embrace gets in the way of something, but it's not super common, and it's got a relatively quick cast time. If it was instant, that would help SCH out, too. The GCD (hers is 3 sec) between uses prevents her machine-gunning them out. One thing about Carby damage, though, is that it can do some silly stuff, like that one World First that was cleared because a Carby got in the final hit when the party got stunned/petrified leading to the enrage. Hilarity ensued, but that kind of thing has value/cool factor to me.
5) DoTs. Are. Dumb. Specifically, DoTs that have no interaction with a kit. You already know my feelings on that. Further, we don't want to add more DoTs/debuffs that clog up the boss's bar anyway when that's already an issue in some situations (24 mans, Hunt Trains, and 48 mans like DR/DRSavage). Besides, you run into the same problem if he happens to be casting to refresh it when you need to use an action AND it would require more AI for him to determine his actions. For example, in AOE, does he roll the DoT across all enemies or just use it on one target and wait for it to expire? With instant cast Ruin 2, all he would do is lock onto the target you attack and use it on CD every 3 sec. There's way less AI programming involved in that. No, it makes far more sense for him to be the ARR Carby we knew and loved.