My friend and I speculated that BUM could work as a "magic tank". Basically it would have abilities like "Runic" that would make the next spell the mob casts target the Blue Mage instead of the other party members (or even the mob itself). This would allow the Blue Mage to learn abilities like "Rhino Guard" or "Cocoon" that normally wouldn't target the Blue Mage. The Blue Mage would also have high Magic Defense/Evasion, allowing it to survive being hit by nasty magic attacks.
For Parties, then, you would still need a physical tank (PLD, NIN, WAR, etc.) but the mob's nasty spells and abilities would target the Blue Mage instead, and inflict far less damage than they would on the tank. It would also reduce the need for "Dispel" and "Magic Finale" since the BUM could prevent the mob's buffs from landing on itself.
Keep in mind that this theory is totally baseless, so don't expect anything of this sort to actually occur. If it does, though, give me some rate ups for being so awesome.