In Final Fantasy (IV-IX) ATB controls when each character's turn goes on cooldown and the speed stat shortens the cooldown. (Spells share a cooldown with Item, change row, etc.)
ATB gauge is a turn cooldown, not a skill cooldown. In most FF games they do NOT use the ATB to limit your ability to use skills. They use mana/MP, which can only be recharged using items, or via resting at a save point.
FFVIII was an oddball one which used a "draw" system instead of mana. I love FFVIII, but its magic system was broken.
Originally Posted by DragonSnooz
In Divinity 2 cooldowns move each turn instead of real time and spells don't have a mana cost (although some spells require the player to spend source).
True. Source could be decribed as a form of mana mechanic. This was pretty limited though.
It's not often I get to talk with another FF fan, so I'm glad you wanted to discuss. If you still want to discuss this after my post, you can DM me so the thread can stay on-topic.
you can't use skills without a full ATB bar (For the entries listed IV-IX). *Player uses a skill and the ATB bar empties. After the ATB bar fills up, the player can use another skill. (Skills such as cover, draw, change row, blue magic, item, attack, steal etc.) In the video specifically ATB is used so Zidane can steal.
All combat abilities use ATB as a resource. ATB limits the players ability to do everything in combat. Compare this to Final Fantasy 1 or Dragon Quest XI, which don't use ATB. For example, stop prevents the ATB gauge from filling up and as an effect, the player cannot use the affected character's abilities. Hasted characters get to take more actions/minute because they get more ATB. More ATB = more skills used, less ATB = less skills used.
By that logic, we already have cooldowns in the game. Every action, spell or thing you do goes on cooldown for 1 turn, then you can do it again. When you are hasted, the cooldown shortens and is skipped every other turn.
The ATB bar is basically your "turn" meter, for when your turn comes up next. Not a cooldown for your skills (the skills that can be compared to attacking, sneak attack, or spells which would require to be restored by resting/mana restoration)
you can't use skills without a full ATB bar (For the entries listed IV-IX). 
