Traditional CC does not fit in this type of game, that's true. This is CC like what the Blue Mage has--optional effects that make up for the loss in damage you take in order to make an enemy less threatening (meaning you have to heal less), and/or speeding up the time needed to defeat that enemy by a greater amount of time than simply attacking the enemy. This wasn't always the case in older Final Fantasies which either had enemies that could be defeated very quickly (thus the benefits of your debuffs not being realized), or the accuracy on those debuff spells was too unreliable, and the loss of damage or healing you took from missing the debuff hurt you more than you stood to gain.

That said, if you have mechanics that demand specific CC, then you can fit that into a game like Final Fantasy XIV. My example of "corrupted aether" from the original post represents this. If an add is designed so that the player has to put it to sleep and cannot deal with it any other way, then that form of CC does fit into the game. The corrupted aether example was for adds that are immune to all forms of damage and will either deal AoE damage to nearby allies or potentially even heal the boss if not put to sleep. If it were me, I'd design it so that this type of add becomes an indicator inandof itself. Any time you see this enemy in a fight, you know to sleep it because that's your only solution.

I know this can also be very one dimensional. It's not very interesting if these enemies can only be dealt with one way, but I'd also consider adding multiple forms of CC on different roles that can be used to deal with these types of adds, such as giving tanks a role action for "Shove," which pushes enemies back. Maybe corrupted aether is always stationary and only damages or heals within a radius of itself, so you also have the option for a tank to shove the add out of the way so they don't need to be put to sleep. Melee and Ranged DPS already have stuns and silences for interrupting, but besides BLM, casters don't really have a way to deal with this kind of thing, so maybe adding Blind as a role action that will cause AoE damage from corrupted aether to always miss.

With this system, you have 3 ways to CC the corrupted aether, and each could offer different benefits:
- Sleep always works, but if you hit the enemy or clip them by accident, they'll wake up. You'll need good teamwork to use it effectively.
- Shove would be OGCD on tanks and thus be easy to knock the adds away, but some fights might not give you the room to knock them away somewhere safe if they're doing AoE damage to your party and thus Shove is not ideal.
- Blind could also be OGCD and will cause AoE damage to be ignorable as it will all always miss, but it won't affect corrupted aether that heals the boss.

This creates a mechanic with multiple ways to approach it, and all teams will always be able to sleep or shove the corrupted aether, blind being optional if the team brings a caster, and each method having a pro and a con.