In regards to the Limit Gauge, generally it's used exclusively by DPS to burn down the enemy quickly right at the end, but there are a few trials where the tank has to use it instead in order for the whole party to survive a phase change (
Seat of Sacrifice after the Quick Time Event when Elidibus summons the other Shards Warriors of Light as his own Limit Break, The Final Day when Meteion literally drops a planet on you to 'end the Universe', spring to mind
), as it's a complete party wipe if you don't.

Players actually had their own Limit Break gauge of sorts originally, it was called Tactical Points or 'TP', and your weaponskills were your Limit Breaks, however because the TP gauge started out full in ARR (you had to fill it slowly in 1.0, as well as FFXI), you could burn through your abilities and rarely deplete it completely, and in the end SE just removed the gauge entirelly, bringing in Job gauges instead tied to certain abilities and mechanics. Hence TP Gauge is gone forever, and Limit Breaks will remain party only/