In 13th Age, the book suggests you can take an uber-powerful Background or One-Unique-Thing if you trade away another power to do it. In the context of Fate, maybe require extra dump stats, or fewer Stunts before taking Refresh penalties?
Well, in the Atomic Robo game (not yet published), you have Skills and Stunts, and you also have Extras.
Characters have 5 Stunt slots.
An Extra takes up a Stunt slot (and there are a couple other prerequisites). Where a Stunt gives only one benefit, an Extra can give multiple benefits. Some Extra benefits also require you take a weakness.
Plus, if a character has more than 5 benefits from Stunts and Extras, the GM gets more Fate points for the bad guys to spend!
So, yes, Atomic Robo is immune to bullets and normal melee weapons. He's also stronger than any mere human. But, he pays for it in that he's vulnerable to electromagnetic attacks (being, you know, made of metal), and the Bad Guys get more Fate points whenever Robo is in play.
Other games have other ways to handle some special abilities. For example, in Spirit of the Century you can make a character like Batman, who can always have just the thing on hand, by taking a stunt, "Universal Gadget". It doesn't give the character *infinite* gadgets that have exactly the powers you need, but if you're pulling them out only once a session or so, you're golden.
You could just ignore all that, and put *everything* in Aspects. But that means the Aspect needs a whole card to define it - "Last Son of Krypton" means *nothing* on it's own, you need a separate listing of what being Kryptonian means, which kind of flies in the face of the intent to make it simple and narrative. Also, the more outright power you pack into Aspects, the more the GM needs to think to make sure everyone's getting a chance to shine, and nobody's abusing the narrative.
I've found it best to have character Aspects that are intended to *modify* results, not to produce results outright.