The trinity system wasn't designed by game developers, it was designed by players. As long as "Make the boss's HP go to 0 before yours does" and "bosses attack specific, nonrandom players" are ideas that exist in a game, the game's meta will migrate toward a trinity system, or will force certain support classes to be in a party.

The trinity makes sense: Imagine we are in a pre-WoW world, where you can allocate your stat points freely. You want the most damage going to the boss as possible, so you put all of your stats in Strength. Your party of 4 goes out to fight the boss, and you do a ton of damage, but not fast enough that the boss dies.

So one of your party members says, "Hey, why don't I just put points into Defense, and take this enmity-generating skill, and then I can survive while you guys deal the damage?" So you go back out, and you survive a little longer, but even though he has points in Defense, your party member dies because your party is now outputting less damage.

So a second party member says, "Alright, why don't I take these healing spells, so I can heal Mr. Defense, and then you guys can deal as much damage as you can?" Lo and behold, you're at the trinity. One tank, one healer, two DPS.

The reason it's so hard to break it is because any "support role" is just to enhance the trinity. Anything that boosts your attack power is enhancing the DPS. Anything boosting your defense is enhancing the tank. Anything debuffing the enemy's attack is enhancing the tank, and anything debuffing the enemy's defense is enhancing the DPS.

In order for a support role to be viable, it has to enhance the abilities of your party members at pretty close to exactly the same magnitude of your lost DPS (because you just can't do it without a healer or a tank, without some massive defense buffs, which would totally imbalance the game). Any higher, and parties quickly become, "[tank][tank][healer][healer][dps][dps][dps][<specific support class>]," and that kind of job obligation is exactly what FFXIV has always (rightly) striven against.

Do I think that support roles could exist in FFXIV? Absolutely, but only because it does an incredible job of making each class play differently. Playing PLD and then switching to WAR doesn't just change your animations and damage/enmity values, it actually makes you completely relearn how to play the game. And when you do learn, you find yourself in the exact same position; you find out that the classes are, in fact, completely balanced. Every other role in the game shares this balance, and it's that mastery of understanding how to balance classes while providing a totally unique experience to each job that gives me faith that SE will eventually introduce a class whose main focus is in managing buffs and debuffs.