Examples of my recent rescue uses:

The Burn (Duty)
1st Boss - when you have a DPS hiding behind the furthest pillar and doesn't know they need to move towards the boss after his arena-wide AoE. Rescue them right into the boss.
2nd Boss - when you have a DPS who doesn't know that one of the five machines are bust and you need to stand on that track - rescue them to the right spot.
3rd Boss - when you notice Mist Dragon's dive-path while a player a mile away is standing right in it without knowing - rescue them out of the dive-line.

Saint Mocianne's Arboretum (Hard)
1st Boss - when the bosses uses devour (leap) to prepare for his AoE across 90% of the arena. Rescue either the tank (if they didn't pull boss to the plant to begin with) or any DPS who haven't budged since the boss jumped.
3rd Boss - rescue anyone who doesn't know they need to stand on pillars during rising poo. Rescue anyone who doesn't know they need to stand OFF pillars during the poo-drop (this one is awkward given you then risk stacking it on yourself and the person, though that is preferable to having 1-4 platforms covered in fatal poo).

Alphascape 1
Various uses here, albeit over short distances. It's a movement-heavy fight so it's possible to save a straggler now and then.

Alphascape 2
Rescuing anyone who doesn't know the dragon-patterns (In, Out, Corners).
Rescuing the rare few who don't seem to notice Midgarsormyr's dive-line during the 'dodge the moving explosions' phase.

Alphascape 4
Pulling someone you hate off the edge after intentionally eating an Omega-F transform push-back, because there always has to be one troll suggestion.