I think a remake of V and VI is just as likely as a remake of VII (though I wouldn't be surprised if VII got it first) and to be honest, Kitase has been doing more executive stuff lately so he may actually have time to stop and come down and work on a few titles, I can see him doing it for VII since the Compilation has been the last project he was creatively involved in.

Of anything, SE has been using the remakes and sequels as a means to train new people so what better way to get the Dissidia team better at their job by having them work on remakes, especially since Arakawa revealed V is one of his other favorites.

With Nomura apparently stepping down from FF titles after XIII Versus gets released to work on KH, it seems to me they may need to build more strong figured in the company to give creative direction since Nojima is freelance and Kitase is basically fulfilling Sakaguchi's place before he left.

Anyway I hope FFvXIII comes sooner than later, and they make a classic FF entry in the FNC series.
Considering XIII still applies the very same formula as all numbered FFs (Innovation), I have no idea what you mean by "Classic". I would say XIII is the "traditional" entry while Agito and Versus are radical departures.