FFIX was made exclusively in Hawaii by a team that was formed there to make the game. This team has now been split in two. Some staff went to form the Kingdom Hearts team in Division 1, while others went to form the Crystal Chronicles team in Division 2. Also, two key staff members, Hiroyuki Ito (Director) and Hideo Minaba (Art Director), went on to join Division 4 and start making FFXII.

So really, there's only ever been two offline main series teams and another one that makes MMOs.

Also, Kitase has confirmed that he wants to compete with this other team making offline main series Final Fantasy  games. He looks at the team as his rivals. He'd much rather not use their ideas and instead make his own. That's why FFXIII never used Gambits or seamless battles.

You barely addressed what I said. ha ha ha

The Final Fantasy series has different teams working on different games. The Kitase-style ones -- VII, VIII, X -- have all a distinct style, but XI and IX are different. XII, different. Is it ever a challenge within Square that the games are inconsistent?

Kitase: They are competing with each other, each team. That brings motivation.

Kitase never says that no ideas can be shared between teams.  Nor did he ever claim that he wouldn't use any ideas from other teams.  Or from games that came before the one he's making. 

He's implying that each team makes gameplay systems purposely different to the other team. Don't be surprised if the next main series FF game by Division 4 has Gambits and ADB returning, especially if Hiroyuki Ito is in the director seat.

I wouldn't be surprised.  I WANT them to use that system again.  In fact, I think that Gambits should be the battle systems' foundation for the next few games as I enjoyed them greatly.  XII's battle system was near perfect in my book.  They only had to tweak it a little to make the player more active somehow (you barely touched a button once your gambits were properly adjusted).

As for the different teams, IX was mentioned, and the battle system wasn't made purposefully different from the other games to compete with them.  It was done the way it was because, as you already know, IX was to be a farewell/hommage to the roots of the series.  As for X and XII, yes, they were different.  But XII felt the way it did mostly because it was now real time.  XIII went a route very similar to XII, as far as the flow of battle is concerned, gambits were re-used in a sense, but were just not programmable.  I think the Gambit system, even though it was almost unanimously praised by critics, was deemed too complicated by a majority of so-called fans who like the melodramatic stories of the games (mostly Kitase's productions) more than the actual gameplay behind it. 

It's no wonder that my all time favorite Final Fantasy games were directed by Horiyuki Ito: Final Fantasy VI (my absolute favorite), IX, and XII.

I think they didn't put Gambits into FFXIII as they didn't understand the programming logic behind them.

Also, if the teams are rivalling then it's a huge ego burst to use stuff made by another team in their game. It's almost like admitting defeat and I'm sure that's something that may have affected Kitase when making FFXIII. There's no way he'd have added the gameplay system of FFXII to FFXIII as that would be Division 1 saying, "You know what? Division 4 has this locked down. Let's just make each Paradigm as customisable as Gambits outside battle and then when in battle you just switch between your customised Paradigms on the fly." It would have been a logical step from FFXII but the sense of rivalry got in the way.

Heck, Taku Murata has said that Crystal Tools caused arguments among Divisions. Staff in Division 1 didn't want to use the same engine as the other divisions as they wanted to be different and not share development tools. Seriously, they didn't even want to use the same fucking engine and another internal team. How ridiculous is that?

Regardless, Hiroyuki Ito will use an evolved ADB system in his next FF. That's borderline confirmed by his Ultimaina interview and his interview in the FFXII Bonus DVD. I'm eagerly awaiting his next game as director. I just hope it has a good, rich and lengthy story to go along with it.