I've done these speed runs with all classes of DPS, but I'm guessing people want them to be extra speedy so they ask for bards/black mages because of the fact they can both do great AOE such as Flare, Fire II, Blizzard II, Cross Hatch, Rain of Death, etc combined with skills like Raging Strikes which increases damage by 20%.

Plus, the bard can sing Foe's that makes the enemies more susceptible to the black mage's elemental attacks.