Unlike the Black Mage, the Red Mage doesn't hit for single digit damage while you try to conserve magic for when you actually need it.

Unlike the Black Mage, the Red Mage can take a hit and not occupy your healer for the next two turns. So unlike the Black Mage, a Red Mage can make a White Mage almost unnecessary.

Unlike the Black Mage, the Red Mage is cheaper as it needs less spells in order to be competent and can equip most of the cool armour you find lying around for free; before then it's no more expensive than a Fighter.

Unlike the Black Mage, the Red Mage can heal more than 30HP... not that it usually needs to.

Unlike the Fighter and the Black Belt, the Red Mage is very useful when it casts FAST on itself.

Unlike the White Mage, the Red Mage doesn't need to selfishly waste time healing itself for the next two turns after taking a single hit.

Unlike the Thief... wait, no. I concede that the Thief, once it upgrades, is better. Until then, a Red Mage can do more than run away.