Actually, Many final fantasy have their own version of 'limit break', though not ALl of it have it.

FFVI was kind of not obvious, you would only notice it if your characters were in critical health, then they would make really strong attacks instead of regular attacks. their attacks would also have names. It's something you would notice if you pay attention.

FFVII: Obviously.

FFVIII: Definitely has it. And I like this FFVIII system too. Basically you get the limit break based on your health, and the lower it is, the more likely you'll be able ot use the limit break. Also, there is a buff called aura that allows you to do so.

FFIX: Trance system. It is based on how much damage you received and deal, it's kind of like TP, but I haven't played FFIX ina LONG time so I can't really say.

FFX: Overdrive system, similar to TRance, kind of.

FFXI: 2hr abilities would be the best way to compare.

FFXII and FFXIII don't SEEM to have something like this.

That said, I feel that FFXIv should definitely have something like this.