Fighters and Knights could beat the game at nearly any level, since their power comes from their equipment far more than from their stats.

I mean, lowest level game means something like level 9-14, depending on how frustrated you get with random encounters you can't run from, right? That means 1 or 2 lv 5 magic spells for a mage. Black Belt won't be able to compete.
And if you are fighting Chaos at lv 10 or 11, you will barely even touch lv 4 magic with a white or black mage. Items will provide all the magic you need. If any.
If you think FAST is important enough to waste a Red Mage on, then get a RM, otherwise, the only party is F/F/F/T