NJClaw
OoOoOoOoOoh
Even if you have other resources, cooldowns can still serve a purpose. Dragon Age: Origins without cooldowns would be a completely crazy shitshow, because they are fundamental to prevent you from going nova.You can have other resources to manage in addition to cooldowns, so that's not an unsolvable problem. You just have to make those resources matter.Another problem with cooldowns, is that they provide incentive to use your spells/abilities with the longest cooldowns first. It's the most efficient output of power, since the sooner you use a spell, the sooner you can use it again. In a resource based system, the incentive is to use spells proportionate to the challenge.
If you already have a resource mechanic, then a cooldown becomes unnecessary. Placing too many restrictions on ability use is bothersome and can become very arbitrary. If a bunch of "tax mechanics" are deemed necessary to restrain a class or spell, then the fundamental design of said class or spell(s) should be reconsidered.
Also, D&D uses cooldowns sometimes, just not that frequently and almost exclusively for monsters abilities.