Yeah, Tulzscha is on the right track. The GCD and cast times are separate things because they serve separate purposes. The GCD is your overall limit on how often you can use a basic attack, and it gives a clear indication of where your weave windows are for oGCD abilities. Every class has this on every basic ability and spell(though some classes have longer or shorter GCDs as part of their playstyle, and some players build to specific GCD values via skill/spell speed materia), as this is one of the core balancing mechanisms. This is not going away, though that wasnt your question.

The cast timer is an indication of how much energy and focus you imbue into a spell before it goes off. Rather then a limit on how often you can attack(again, your GCD handles this), this is a limit on what you can DO. You cant use another ability while channeling a spell, if you move you risk losing the cast, sometimes being hit violently enough will interrupt the casting action. And even more so then different classes having different GCDs, different spells have different cast times. You see some spells cast instantly(cast while on the run, more or less uninterruptible), others with cast times shorter then the GCD(which allows for some movement or a small weave window in between casts), yet other spells with cast times equal to the GCD, and many of the strongest spells actually have cast times LONGER then the GCD. This encourages different strategies for when and what to employ. A Black Mage getting ready to cast Flare(4s cast time) and a Summoner casting Painflare(instant) need slightly different mindsets and preparation, even though both are executing AoE attacks they learned at or near level 50.

This is acutely felt by healers. Needing to know when to use a full cast spell, when to use a quick cast and weave in an oGCD ability, and when you can ignore the damage for another round or two(and maybe have a better ability available to use). This level of understanding of their kit is(one of) the difference(s) between an ok-to-good healer and a great one.

So to answer, could they remove the cast timer? Of course. Not every spell has one, so clearly its something that could potentially be removed. But they arent likely to, because the timer serves a different purpose then the GCD.