Again animation lock is only on two things. LB, and moving. Now it sucks for dragoon. But if you never play dragoon, the player might never even seen it beside LB. But LB is purposefully made this way, it also makes perfect sense for most people, you can cancel the LB cast, but once you have casted it, you are locked into doing the full animation, its the entire purpose of LB, its a huge finisher in final fantasy games, usually very cinematic, if anything being able to cancel it, makes it a bit too strong. I mean being able to finish 5% hp of a boss or rez and fully heal the entire group, is a very heavy and strong ability, making it the only hard part to manage where/when do i start it, is more about fight knowledge. When animation lock is a problem is for the movement spells, which is pretty much almost all dragoon, which really sucks. So if you encounter someone that doesent feel animation lock ruins it for them, chance are they just never played dragoon lol. Most people wouldnt really think LB lock is a thing, it make sense for LB to be like this, specially LB3, thematically and just mechanically.
And my gif is showing animation cancelling, Animation cancelling is just how its named, you cancel the animations. As my gif shows, my abilities dont have all the time to finish before the new one is shown. Its super evident in the first global cooldown, where the second ability stops the entire animation of the first one midway.