How exactly would you have a cool down system in a game with turn based combat? Time is essentially frozen during the round, and each turn is like 6 seconds of real time.
TBH FFIV-FFIX, XIV all have cool down based combat. ATB is essentially cool down based (derived from speed stat).
This isn't quite what cooldowns would mean. Final Fantasy games typically use a mana-based system for skills/spells.
Larian did skill/magic cooldowns previously in DOS2. This is another reason why we're unlikely to see the introduction of skill cooldowns in BG3. They're already being accused of making BG3 too similar to DOS2.
A cooldown in a turn-based game basically means that once you use a certain skill, you have to wait for an certain number of rounds to pass before you can use that same skill again.
