What class best fits description

Just happened to be thinking during my long dps queue...

What if they introduced a class that has a certain buff/mechanic that allows it to have very short cooldowns, but the cooldown time doubles after ever 2nd skill?

For example: Skill 1 (1s GCD)- Skill 2 (1s GCD)- Skill 3 (2s GCD)- Skill 4 (2s GCD) Skill 5 (4s GCD)- and so on and so forth. While its good in its first few skills, it can still be strategic.

Im sure theres much more info that should go with that, but just something I was thinking about. Would any FF occupations you know of fit this description?

A support class i would say maybe Corsair http://wiki.ffxiclopedia.org/wiki/Corsair