-Point of notice: As you'll play through the dungeons, you'll find the 'sweet spots' where certain spells are more useful than others. Cure III has a place.-

Useful and general instances:
  • When tank pulls >5 adds, WHM steals 1/2 of them. Self-cast Cure III in proximity to the tank and wait for Flash Spam to take back the adds.
  • Titan
  • BCoB enrage timers
  • Ifrit Ex group heals when searing (Target DPS)

Someone has rightly pointed out overcuring as an issue.
However, simply waiting an additional tick for aoe damage to turn over can make a Cure III worthwhile and cost-effective.

Turn 2 enrage:
Wait 1 pulse, both healers cast Medica.
Or
Wait 1 pulse, WHM1 Cure III
Second pulse, WHM2 Cure III
Alternating.
It's easier, and mana consumption tends to be better.

1 Divine Sealed Cure III can restore almost 80% HP of a group.