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None of its spells have individual cooldowns, its simply a global 3 second cooldown.
This means for healing Choco Regen (needed) and Choco Medica (Not needed) are just poor spells.
Theres absolutely no benefit to using them 90% of the time over Choco Cure and the AI makes poor choices.
This is why you only get the skills and abilities you need and avoid the rest. It's not ideal, but it's useful. Change to healer mode to have your chocobo spend more time healing, and require a lower health loss threshold before it starts healing you.
Personally, I stick to level 6 healer, and level 9 attacker. That way, my chocobo only uses Choco Regen (decent), Choco Cure (very good), Choco Slash (meh), Choco Beak (excellent), Choco Rush (pretty good) and plenty of buffs.
I see most people doing 7 points in Healer and then 2 in each the other ones.