Specifically, it's really annoying when you're trying to chase a healer who is almost dead, and you go to hit Sprint, but since your GCD didn't quite reset yet, you didn't Sprint. Of course, maybe you just hit Invigorate right after to get TP, but that was now pretty stupid because you're not Sprinting. Not like it matters, because since you didn't Sprint when you wanted to, now the healer is around a corner and healing himself. I run into this problem a lot when trying to shoot a Blast Shot or Far Shot as well, in addition to other buffs. I'll frequently press a buff or off GCD attack, think it went off because I clicked it, and then go back to my normal attacks... then often see that it didn't go off.
I could, I guess, make macros for everything that tries to cast that ability 5-10 times with a very small /wait between each one, but that's kind of ridiculous.
Either buffs need to queue up better (e.g., if I click Sprint during Heavy Shot animation, Sprint always goes off after Heavy Shot is done instead of giving me an annoying message that it's not ready yet), or buffs need to go off regardless of being "animation locked".
This is actually mildly annoying for PvE as well, that you need to weave buffs in-between attacks to try to avoid a loss of dps. If you knew nothing about the game system, you'd think as a BRD that if you wanted Raging Strikes and Barrage to be up, you'd just hit Raging Strikes and then Barrage, whereas in reality you want to hit Heavy Shot (or whatever), then hit Raging Strikes after the Heavy Shot animation ends but BEFORE the GCD resets, then Heavy Shot again, then Barrage after Heavy Shot animation but before GCD reset, etc. If you hit more than one buff in a row, you're going to lose some dps because you wanted a chance for you to do an attack.
I'm not sure exactly what's the harm of a buff interrupting an animation and just going off instantly. If I want to quickly Raging Strikes then Barrage between attacks (Barrage interrupting the Raging Strikes animation so both buffs go off super quick, then interrupt Barrage animation to do a Heavy Shot), is that really the end of the world? The way the animation lock system works seems to be an unnecessary inconvenience.
What's worse is that sometimes buffs don't even proc instantly (the worst is using Hallowed Ground and then dying - recast is used up for it so it clearly went off, but yet you still died... sweet). Many times I've used Swiftcast as a BLM and then had the next cast go super slowly because I hit it too fast. Well, a lot of problems are going to occur in PvP if they are related to "doing something too quickly" because the entire point is to do everything as quickly and smartly as possible. Otherwise, that other guy is going to get around the corner and heal up. You have to be super fast, and if the game punishes you for trying to go fast, that's not a lot of fun. Is the intention that after I hit Swiftcast, I wait for 0.5-1 seconds or more for the game to figure out I actually used Swiftcast? (This sometimes happens with spells, as well, where you see the animation for Blizzard III going off, making you think you cast it, but in reality it didn't go off - because the monster died, or you got otherwise interrupted at the last moment.)