I hate having to have another character finish the mess when one combatant doesn't kill a monster that it should have killed.
Your asking for the Red Mage to become a uber melee. That's not what they are, they are a mix of magic and fighting, not as good at fighting like the monk and warrior, but having the magic to heal and nuke when needed. If your complaining a Red Mage can't kill a strong monster in one hit like the melee, might as well complain Ninja can't kill them in one hit, or Black Mage, or White Mage.

The thing about a Red Mage it is meant to excel in fighting over the other mages (which it does) but not be so godly strong that it IS a melee. And on the other hand it casts magic but so much that it becomes only a mage. It's a mix of the two and that's why it's such a good class, because you get a guy who can whip out a FIR2 to decimate the enemies, then a CUR2 to keep your tank up, then bring out his sword and conserve MP will still doing some good damage to the monsters.