There is nothing in this game that punishes mages anything like amnesia punishes melees (and tanks). This might be due to how hard it is to punish the BLMs while still letting the healer do their job.
I'd imagine outright magic immunity would do that. But that just ends up being no fun for anybody, since nothing would die in much of the current game design. Mute would do just the same, but then you'd end up relying on alternative healing sources, such as a DNC (which, admittedly, sounds like something we ought to see more of if they felt like balancing content so), or a SMN with a healing avatar already out, or BST using a rarab pet. But then these options all fall prey to the same disadvantages of melee damage dealing.

The other thing about how content is designed is that, when mages are disabled, it's often far worse for the party than when the melee are disabled. If a melee is under Amnesia or even dies, it's often treated as a minor inconvenience that is resolved with the passage of time. When a mage is disabled, it's a huge setback for which, if there is no backup, the battle might even be considered a loss. Same goes for tanks. Imagine if they were tasked with updating the jobs such that we find ourselves one day saying, "Oh crap, the MNK died! This is a disaster! How are we gonna recover from this?!"