Damage / Buff calculations based on animation is problematic.

[Altena]

The description actually says that the "cast time" is instant, which it is.

SE could change all these abilities to be actually instant (Aero surely feels like it hits instantly if I'm not mistaken), but its also true that the playerbase could just accept how these abilities work in the game instead of demanding that they be changed.

Aero feels instant because there is no wind up animation / Aero doesn't have to travel through the air to land on the target. It just hits the target immediately. The animation is also extremely short. It is also an insignificant issue for a spell like Aero.. The issues are on a completely different level when you are talking about mitigation skills on PLD (which could mean life or death) as one small example.

Asking players to accept it, is asking us to accept poor design and response time..

There are 2 potential cases..
1. SE don't know how to fix it.
2. It's a design choice.

Both are terrible.

I also disagree with saying that the current system is "unresponsive". Unresponsive would be you using an ability and it only starting a few seconds later.

Well this can also happen.
Along with complete animation cancelations.
Use a skill, half the animation is displayed, half of the GCD completes, then you find out that the skill didn't actually go off. This happens quite frequently with Shield Lob.
So yes, often skills are also unresponsive, which is another glaring issue entirely.