Sidenote: in the case of Golden Sun, the working theory wasn't so much "djinn of their element, it is easy and sensible and makes them not suck". Due to the way GS handles skills and classing, the initial levels in an element for each character combined with piling all their own element Djinn on them leads to each character getting a unique class with... one or two unique skills, is my memory? But the unique class thing was what stuck with people. It's possible there's other unique class/skill combos within the system (I don't know really, but it seems likely), but since only a handful of people played the game (and none of them really care about it), the whole "thoroughly explore alternative setups" movement never touched on them.
Yeah, basically. All classes in the game are shared by 2 PCs at least, IIRC (typically Isaac and Garet share classes, Mia and Ivan share classes), but if you give all Mediums of a single element to that respective character, it gives them a unique class. Golden Sun 2 was the same way, just with double the Djinns, which means there's an argument over who gets what for characters like Felix vs. Isaac (note that even in GS2, some unique classes exist. Both Fire and Water Adepts get different classes, IIRC, since they basically swapped roles in GS2, so your Water Adept was the Tank Fighter and your Fire Adept was the Mage, where as Garet and Mia were the other way around), though, there's an easy tie breaker I applied in my stat topic:
GS2 characters get all Djinn before the GS1 cast arrives. GS1 cast gets all the mediums they come with; technically a transfer data thing, but its more a balance purpose thing, and then gets the next 4 mediums (one for each element) that not only appear til after the GS1 cast appears, but requires map abilities that the GS1 cast brings along with them, so yeah. Anything after is kind of illegal, but I think they have enough Djinn to access their new ultimate classes, so its just "minor stat boosts" here, and one less unleash.
FF8...is probably the single worst game to give a character one thing but not others. True, WA5 characters suffer by Carol getting Luck, for example...but that's really no different than Carol just getting an extra awesome accessory; she gets significant stat boosts to 2 stats, and that's it stat wise, and some indirect abilities that help her independent dueling style, while doing little to the cast as a whole (don't think her damage is helped TOO much. Life Drain may do more, but its not as big a jump as, say, Greg's Hi Crush.)
FF8? Give Squall GFs only and...oh shit, now his stats sky rocket to hell, and he becomes a OHKO machine with like 3x the durability of everyone else ON HP ALONE.
FF8 played under the assumption that everyone would have at least one GF. The game hands you two before your first mission, and right before you get your first 3 man party, you get your 3rd GF; from here on in, you're never caught in a scenario where you have PCs without junctions, one exception is the final battle due to the nature of how its structured.
Now, look at FF7. Cloud getting Lightning/Ice Materia means...nothing other than his damage will never drop below a certain point, and now he can do stuff to people like Kimhari (limits accepted). Red XIII's Fire is just an extra damage type for him to get, one which hurts his main damage too I should note. Yuffie's...is almost completely pointless, and Cait Sith gains a status. It does little to effect the other 5 PCs, just arbitrary advantages that help their dueling style to varying degrees (Cait SIth's is a huge boon, for example, Yuffie's not so much.)
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Now, FF6plot claims that are remotely reasonable. I'm not suggesting people allow these, just tossing them out since they were brought up. Note some of these are incredible stretches, and I am not trying to make any reasonable claim about them.
Terra:
Ramuh (rescued her, watched over her before your team joined, etc.)
Tritoch (The entire early game nonsense)
Maduin (most obvious one)
Fenrir (dropped by Phunbaba, thus related to the Mobliz stuff)
Odin/Raiden (TERRA GETS A UNIQUE LINE OF DIALOG IN THIS DUNGEON IF SHE READS THE QUEEN'S DIARY!!!)
And based off Dissidia, you could argue Phoenix, cause her Crystal is a Red Magicite which has a big bird that resembles a phoenix on it!!!1 Interestingly, Phoenix is one of the Magicite that is most like Terra's current natural magic set, meaning she gains so very little from it, so really, this point is almost completely useless (idly, Terra does naturally learn all spells from Ifrit and Ragnarok! no, don't know why I brought this up...)
Locke:
Phoenix (self explanatory)
Ragnarok (Required to get the darn thing)
Celes:
Palidoor (on Solitary Island; this is the closest we'll get to a "place of residence" for Celes, unless you count the factory, and by that logic, Terra should have access to all Espers there too...)
Mog:
Ramuh (is the one who taught him how to talk, and told him to join the party, apparently.)
Terrato (Terrato belongs to Umaro, who can't use it, so clearly, Mog deserves the damn thing.)
Cyan:
Alexander (Found in Doma, but only after his Dream sequence...you can actually see the Magicite in the Throne Room after Wrexsoul is defeated oddly; probably has to do with some trigger nonsense or it was the game's way of going "HINT: CHECK THE THRONE ROOM AFTER THIS SCENE!")
Relm:
Starlet (Chardanook nonsense)
Setzer:
Bahamut (HUGE STRETCH. Doom Gaze is fought on the Airship only. Airship = Setzer, thereby, Setzer gains this!)
Shadow:
Gilgamesh (FF6a only; he's fought in the Colosseum, thus belongs to Shadow!!1!!)
Like I said, a lot of these are stretches and not really reasonable at all, just tossing them out there.