What if...

[kyuven]

That and... Do we actually need it?

Haste, HP regen, accuracy, defense, elemental resistances... There's a lot of potential to make bard a class that actually uses songs.

Pretty much this. While HP regen might not be a great idea since it would either be too powerful or too weak, there are a lot of "holes" in what bard classes in other games can do that the bard job in this game can't.
Haste, resistances, accuracy and a physical damage debuff immediately spring to mind. The Mudra mechanic can easily be tweaked and adopted for the Bard job for at least adding some elemental resist songs.
But then again even for being a "boring" class, Bard is pretty powerful and valuable simply due to their mobility, so this would probably be something for 3.0.