The thing about Red Mage in FFXIV is that they could design it to fit most of the roles available in the game.

Healer with some offensive magic (ranged from safety) or melee (higher DPS, maybe mana regen?)

Pure DPS that mixes melee & magic with some limited healing/defensive magic (like how a SMN has physick/raise)

Support DPS that mixes melee & magic with minor group wide support abilities (think a melee version of BRD)

Or a tank that uses defensive white magic & melee with some limited offensive magic power.