Personally, I think a 2.0s GCD is about as far as it ought be reduced at base. Competing MMOs with such short GCDs also rarely take around a half second to complete their skill animations -- ours, on the other hand, are quite a bit more complex.

That said, even if you scaled animation times with attack speed, at 2.0s you're already risking removing double-weaves for many, many players. Which then leaves you the question, do you want to remove the only unique thing XIV gameflow has, double-weaves and the apm (actions/keystrokes/presses per minute) dynamics of double-weaved openers to the slower lull of having everything on cooldown -- likely decreasing the apm ceiling, in the process -- in order to increase the apm floor?

Removing animation locks entirely would only give us a flurry of disjointed limbs as animations clip wildly into each other. That would look fairly awful, and would defeat the point of having our more detailed animations in the first palce. Certain animations made to have multiple clipping points and starting points as to more quickly and smoothly clip into each other, alternatively, would be great, but there's a reason that oGCDs in most games without animation locks... also have no animations (at best surrounding visuals, rather than manipulating the character model). Some of our animations could probably still look good as mere surrounding visuals, requiring no animation lock, or similar animations for different abilities could combine the animation while carrying both effects, but that would of course add complexity to memorizing what you can and can't double-weave, with all others having already been removed...

:: I have heard plenty of complaints about the relatively long GCD by players who haven't hit 50+ yet, and therefore (1) haven't filled out their hotbars yet, and thus lack the oGCDs to fill up a lot of those gaps, and (2) haven't seen enough fight complexity to ever make them glad they have that extra second to look around, check their CD syncs, etc.