Sue the zombie dinosaur comes to mind. Like the note says, the power is mostly unsuitable for player characters. But it's good for zombies and golems and inanimate objects being modelled as creatures.
I don't have difficulty coming up with characters who could conceivable have a power to represent their 'mindlessness', what I have difficulty with is conceiving of a character incapable of executing any trapping of a skill that the GM concludes 'requires thought'. The problem being that that variable is wholly undefined. From a player's point of view, then, until it has been defined, or at least refined, it must be assumed to be as punitive as it could possibly be.
I cannot conceive of a character that could function should the GM, on a whim, decide that using Fists to attack requires thought, or that using Athletics to overcome physical obstacles to movement requires thought, or that using Investigation to locate the source of a scent requires thought. All of those things, for humans (which, I'm pretty sure are the go-to example of 'thinking beings' these days), require thought, even for highly trained experts, to some minimal degree.
I have difficulty conceiving of a functional character that cannot perform the most basic of tasks.
What if the bans were replaced with big penalties? Would that be workable?
I doubt it, but if you write something up, maybe you'll prove me wrong.
See, I don't really want to make having no brain super expensive. So I need to balance out the mental invincibility somehow. And I don't like the idea of having to find an in-game justification for when Sue refuses the "you can't do occult research" Compel.
Well, for starters, I'd ask the player how they think they're going to justify having points in a research skill in the first place, and then wait to be impressed. I'd do that during character creation. Because Sue does not seem to be the Brains-y type.
After the compel was in play, though you'd deal with it in the same way that you'd deal with a BCV refusing a 'the sun is rising' compel. Find whatever flimsy excuse you need for that situation simply not to inconvenience the character.
These problems can solve each other. Sure, the Mindless Power will be unsuitable for PCs. But nobody (that I've ever heard of) wants to play a character without a brain anyway.
As I believe you've pointed out yourself in the past (or it might have been someone else and I'm confused), simply marking a power available only to NPCs does not make it balanced. Rather, it demonstrates just how UNbalanced the power actually is.
Oh, and the Superior Programming thing doesn't present any problem that I can see. It lets you do something that requires thought without thought. Doing the impossible is standard for Powers, right?
If you don't think a paradox (something that, by its own definition, can't happen, rather than 'magic' which merely defies conventional understanding) is a problem, how about a simple costing conundrum?
How many trappings do you imagine could possibly be barred by Mindless? How much refresh would it cost to gain immunity to mental stress? How much refresh would it cost to overcome the drawbacks of Mindless, a power which offers no benefit beyond mental stress immunity, but includes a significant drawback (something generally represented as affording a rebate)