Probably for the same reason as a thousand other things in the world. Money.
True, but part of that is restoring the Final Fantasy brand. They are pretty ashamed of the shockingly bad FFXIV release (and FFXIII to a lesser extent). They know it's damaging their company.
They made a public apology, they made the game free to play for a long time because it was so bad, and they have spent the last few years not only maintaining the current version, but building an entirely new game that everyone will get for free (everyone that bought the original). They even make development decisions based on player polls, and made a forum to gather feedback, which is all pretty unheard of for Square.
Honestly the new dev team behind FFXIV ARR deserve nothing but kudos for their efforts. There is actually a lot of positive buzz about ARR in the MMO community too, who are all sick of WoW clones. It'll be released on PS3 as well, which is really lacking in MMOs. It'll be good for everyone if this goes well, I hope it does.