I cannot agree with the user that stated Red Mage does not need a buff. Just because it is a simple job does not equate it should not do more damage.
For ARR and a good portion of HW Bard was very simple..
Which brings up to the other point, utility wise other then raise what does Red Mage bring? Some are so big to point out utility but embolden is not big enough of a contribution.
Jobs like Bard bring far more utility and does do more damage (this could be debated mind you). So perhaps slight buffs and changes need to be made. Higher cost for verraise, and certainly changes to embolden.

As for movement, it is not of issue like that of blm, then again smn is not really hindered by movement so much either..

The only bad part is if you mana shift and say use Lucid Dream (the amount of times i need to raise healers) and then for whatever reason get killed, Red Mage is then completely out o f mana once raised, so another form of regaining mana perhaps could be nice. This is about one of the only situations were your dps could drop down.