As much as I sort of like the idea of a tactical "uh-oh" button. From a game design perspective it's a huge miss-step. I remember SE commenting to the effect buried way back in the annals of FFXI official comments.

Any end-game content has to be designed under the assumption that every party member will have access to their 2-hour, as to do otherwise would trivialize the content with the use of 2-hours. But by balancing in that manner, you make all content have a unintentional mandatory 2-hour cool down. It can be worked around by artificially extending the length of the battle (longer battles reduce the relative effect of any single action). But it effectively tied SE's hands and forced them to do much more work per encounter than was necessary.

Before people jump on me saying that it wasn't that way at all. I was speaking about very early on in the game's life. SE "solved" the problem by slowly trivializing the 2-hours to the point where they were rarely worth the time it took to use them, which kind of defeated the purpose of them.

I think this Limit Break system is a much better approach to the same idea. They can balance battles around the assumption that eventually any given party will be able to shoot off a LB without the same temporal restrictions.