In an interview with Next-Gen, Final Fantasy XIII-2 Producer Yoshinori Kitase says that Final Fantasy franchise may take a shift into action-RPGs due to their popularity:
I think the nature of the franchise is to present something new each time. In the global market we see many players moving away from games that used turn-based systems toward what you might term an action-RPG.
That's a trend, and you ignore things like that at your peril.
FFXIII and FFXIII-2's battle systems have those elements of speed and action that are the key words for us, though that doesn't necessarily mean we're going to stick to the same route in our next game. That's something only time can tell.
Well, it's not like Final Fantasy has been keeping with its turn-based roots for the last five years. Final Fantasy XI was a MMORPG, Final Fantasy XII had the gambit system, Final Fantasy XIII was quasi-real-time, and Final Fantasy XIV was... something. With the success of Kingdom Hearts, I'm surprised the franchise hadn't become an action-RPG earlier.