They're supposed to be a fragment of the Primal's power. It also appears that the primals themselves can access this very power (Titan and Ramuh summon Egis themselves)
Also I swear Shiro is adorable in that scene
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Re-sub re-sub re-sub! Titan-Egi is the best tank for King Mog Extreme!
Well you are entitled to your opinion, but that doesn't make you right.
Titan can tank whole dungeons if you use him right, with cooperation from your healer. The only set back is that PS3/4 players don't seem to be able to target Summoner pets, where as PC players can by clicking on them. That aside, I've used my Titan numerous times to tank level 50 dungeon mobs and bosses. I'm not saying it's as good as having a Pld or Warrior, but it is a viable option if for whatever reason your tank bails. You'll need decent gear though, or like others have suggested, summon him with +vit gear on.
Heck I even had a real fun time once in dungeon with another Summoner and a healer (can't remember which job they were) after our tank bailed at the start of Lost City, we managed to kill the first boss before another tank finally que'd in. That was probably the most fun I've had in a dungeon in a while.
I will admit that once you get the Garuda minion, Ifrit essentially becomes obsolete. But I believe they are buffing Ifrit in 2.3, haven't really compared how it will stack up with Garuda yet, but it is what it is. Right now the only time I generally use Ifrit is if I get CM on my main scenario duty roulette and I get beat to the cannons have to melee, because I can use Ifrit to stun the Colossus effectively.
As for their appearance, I personally like them. It works for this game and I find them pretty artistic creations of the primals they represent.
Titan-Egi is a decent tank, it'd be nice if he had a way to quickly move up the aggro table but other than that I think he's pretty much fine. No one should want him to be as good as an actual PLD/WAR though.
As for the appearance of the summons, it'd be nice if they were a little bigger (or grew bigger when using Spur.) But other than that I actually quite like the stylized appearance.
My wish is that they would change titans model to that of the adds in extreme titan, they actually look like titan, unlike the giant crusty popcorn we currently have, as for useless though, none of them are, Garuda is always useful due to contagion , ifrit can be preferable in some fights, and as others have said, titan can tank dungeons if you play it right, I've run a few where tank left due to not liking the one that popped, and 3 manned it with titan .
Fun fact: Magitek reapers in Hydaelyn are the exact make and model from the ones found in FFVI's universe, specially one a certain Tina (Terra) Used. Another Fun Fact: You stated "fragment of power", there's no true difference between 1 fragment of power and another another - a fragment is a fragment, same concept - You're not wielding the full power of the summon.
Another fun fact: The Crystal Tower originated in FFIII's world, which had no Allagans. Another Fun Fact: A couple of Garlean soldiers admit they came from Dalmasca.
I get what you were trying to say but the point is, having a fragment of power isn't truthfully an excuse for the design we got when their previous FF MMO shows they could have done much more if they truly wanted to using the same concept. :p