The first time I ever watched Final Fantasy: Advent Children, I thought "WOW, why don't they make Final Fantasy games with combat like this?!"
Well I think it could be possible with FF-XIV.
It was done slightly in FF-XIII by way of staggering you're opponents then launching them into the air leaving them vulnerable to attack, and then being able to jump up to them (a pretty nice jump I might add) and air attack them.
It can go further with FF-XIV.
I just have 3 Suggestions for now:
1: Enemy/player(if added) knock-back skills - When an enemy knocks us back, we shouldn't just slide across the ground like we are on roller blades or something. Depending what kind of knock-back blow it was, we should either be knocked off of our feet while we fly back, or knocked into the air where we will then recover with a cool back-flip of sorts. Special Physical attacks should become block-able/parry-able, in which we then become partially staggered, and not being knocked back as much. Player abilities to stumble/knock enemies back should be implemented as well. Pugilist, marauder, and shield already have some attacks that should have a knock-back/knockdown component. Some can be added to the rest of the battle classes as well, instead of just "stunning". Like Lancer's Leg sweep could knock the enemy down for the duration of the stun, instead of them just standing there stunned.
2: Jumping - If or when jumping is implemented, it should be able to play a huge role in combat, and not just be some weak 2 ft jump. We have already seen sorta how high people can jump with Seismic shock and Arrow Helix. During combat, we should be able to jump even higher, Over the Great Buffalo even, maybe even expend some TP to make such jumps. Like we see the enemy about to perform a special that we know will only hit from the front. instead of just running to its side or behind it, we could jump over it completely. Also jumping can open up new attack motions, New attacks, and Actually look like you are reaching the body part you are attacking (Great buffalo horns). Seismic Shock and Arrow Helix could be abilities you use after jumping.
3: Enemy skill usage - Lots of enemies have skills that take some time to go off, but when they do they are sometimes just 'meh, weak', like Great buffalo's Stomp. Why does it have to charge that up? and why does it do the same amount of damage as his normal aoe-melee attacks? Monsters' charging attacks should make a player think 'omg i need to get away from this thing nao!'. And need added instant-skills that are not so deadly. People would learn to move out of the way. However it is known that since EVERY ACTION you make stops your from moving your character around, changes like these would most likely just get everyone killed before they even have a chance to move. But once players have more freedom of movement during attacking and skill usage, Monster attacks can definitely become more powerful.