I already die to the enemy dragoon's LB on a regular basis. I can't embarrass myself even more by dying to our own dragoon's LB, too.
(Jokes aside, this would make AoE jobs unplayable in CC, esp. on those small maps with narrow paths that are sometimes completely covered by some AoEs. When everybody is on the crystal your AoE DPS might accidentally delete your own team, esp. when we are talking LBs. Think of summoner, redmage, dragoon, black mage, paladin, white mage, astro, scholar, gunbreaker, pictomancer etc. That would be chaos.
Healer stonks would rise but you'd basically need fixed role queues to ensure there's a healer on every team for any kind of fairness. And even then I don't think healers have enough healing in ther PvP kits to deal with twice as much AoE damage.)