When they aren't recovering MP, they will consume MP faster because with a group healing song up and healing a tank, they will burn through MP faster, making them have to balance appropriately.

Now, for the addition of an actual separate job. Please... give... me... a... real... DPS! Bring back the Sniper or Ranger. Beast taming would be a welcomed new idea as well. I believe people will recall the Beast Master from FF11, but considering the great solo play capability of FF14, I don't see an issue with Beast Masters here. For lowered agro reasons, I'd say Beast Masters would be great (agro shared between two targets) but for the flash and enjoyment of high damage, I like the idea of the Sniper.

Anyways, there's my recommendations. I think a new healing class made out of Bards would be very interesting given some proper changes to their skills for balancing.