As far as I can tell, your physical distance from a mob only matters for initiating auto-attacks and not executing them. If you're far enough from an attacking mob, the auto-attack won't be initiated until it gets into range. However, once you see the mob pause to 'cast' the auto, it doesn't matter how far away you are, because the attack is already snapshotted to you.
The same is true for tankbusters as well. If you move away from the mob, it will wait to catch up to you, pause to start casting, and then the attack lands regardless of how far away you get in the interim. I think that an auto is just a unique case of a 'cast' that has '0' cast time, but still takes a non-zero amount of time to cast because of execution issues.
The responsiveness of a mob depends on how far away you can move before it also starts moving to close the distance. In Warcraft, that distance is really small, so it feels really responsive (you also were able to force a mob to backstep by entering into its hitbox). In FFXIV that distance is a lot bigger. That's why FFXIV's mobs feel a lot less 'maneuverable' to drive around the arena.
I think I know the reason behind why this critical movement distance is set so large. It comes down to 'casts'. You've probably seen this yourself, but if your character is moved a sufficient distance while casting a spell due to a movement effect (knockback/draw-in/etc.), it interrupts your cast.
In ARR, you could interrupt mob abilities this way as well, including abilities that you weren't actually supposed to. The Wavetooth Sagahin in Leviathan Ex uses an uninterruptable Dreadwash as a roomwide fear. It was likely intended as a mini-enrage, which is why you couldn't interrupt it. However, any action that displaced the mob (classically getting your WAR to Holmgang and jump away, pulling the mob with them) cancelled the cast. I suspect this was the reason behind the 'Spin' glitch back in ARR/Heavensward as well, given that a mob that is constantly being moved is unable to initiate a cast. I think that's the primary reason why all player knockback/draw-in effects were removed in PvE over the course of Stormblood.
I think that the reason why mobs are coded to be relatively 'movement-insensitive' is because they probably found that movement jitter from the player was preventing casts. I personally don't mind if a mob autos me from across an arena. It's not really immersion breaking, and you're really not supposed to be able to 'kite' a raid boss by outdistancing them. What I do want to see are mobs that move the instant that I do.