I never understood the issue with cooldowns. Underrail has them and they are fine.
They're bad because they force the player into a rotation: You'll always start with the strongest ability that also has the longest cooldown, and work your way downwards in order to maximize DPS. Instead of having all moves available at every turn, allowing the player to choose the smartest tactical choice for the circumstances, you will most likely have figured out the perfect rotation of moves and just keep going with that no matter what.
They're also a ridiculously arbitrary way to balance a game, see the absurd grenade cooldowns in Underrail. In what reality does it take 4 turns to reach for another grenade? If they are too powerful, just make them rarer and more expensive. Cooldowns are the lazy way out.