That wouldn't be a rebirth, it'd be an execution.
There's a lot that could be done to update the FFXI engine into FFXI-2, though. Making the baseline standards for modern PC's/PS3/XBox, including data transfer and all else would leave the devs considerably less constrained in developing the game further.
Then just give us "legacy" items to pass over to the new accounts that increase in power as the character does, whether simply as a reflection of the character's job levels or as a series of upgrade quests.
Say, if you'd done Warrior to 99, you'd transfer over with a "Old Rusty Greataxe" that's Rare/Ex, Lv1 with modestly nice stats for a L1 character- the equivalent of a decent DMG/Delay with STR+1 or something. But at 10th, you find some nice Moogle in town who can polish it up. Now it's a good L10 Greataxe with better stats. L20, someone in the area you're leveling up in offers to restore that wrapping on your old axe's grip. And so on, and so forth. Legacy characters would have additional "AF" storylines to go through related to their old jobs.
The heart of the game is still sound. Getting an opportunity to modernize it from the bottom up would give you a 2014-2015 era game- graphics, story, and all.