But how do you define what powers a spellcasting character has in the first place? What's within their theoretical capabilities? Presuming that their character has some idea of what they're capable of, wouldn't that mean that they have an idea of what range of results on a die roll constitutes success, rather than whatever the referee thinks is accurate? Is there a limit to how much magic they can use over time? What's the rest/recovery rate for it, etc.?
Depends on the world.
Take something like Marvel superheroes. Okay. You're playing Human Torch. What can he do? Fly, shoot fire, flame sheath, make constructs out of fire, go nova, things like that. How much fire can Human Torch put out in a day? It doesn't matter. What's the rest/recovery rate? Doesn't matter.
What can a D&D-style spellcaster do? Depends on what you want to do. Do you want to be a necromancer? Then you can do that stuff. Do you want to vampire-like drain the life out of someone from a distance? Cool, roll it. Do you want to raise the corpse of the monster you just killed to fight by your side? Cool, roll it. Do you want to speak with the spirits haunting this place? Cool, roll it.
FKR is about emulating the world, not fretting about mechanics. Because, importantly, the mechanics cannot possibly emulate the world...no matter how complex. Build the world and the magic system to a point where it's coherent and makes sense, then you'll have your answers. Hint: it's not about spell slots, die rolls, or rest/recovery systems.
I suppose what I'm trying to say here is that FKR sounds like it's based heavily on a referee interpreting things based on how they think the world works (as per the experienced generals who didn't need charts and tables to figure out how things would proceed during an actual battle). But magic has no real-world equivalent from which to draw, meaning that the referee seems like they'd need to do a lot of heavy lifting (which also seems to run the risk of straining the burden of trust placed in them) to make it work.
Just like you'd have a Session 0 to get everyone on the same page in D&D, you'd still have a Session 0 to get everyone on the same page in an FKR game.
But you'd start with the world instead of the mechanics. If you wanted to play Mistborn for example, then we'd reference those novels and the associated wikis to work out how magic works. If you wanted to play Marvel Superheroes, then we'd reference the comics or films and the associated wikis and go from there. It's nowhere near as hard as people make it out to be. You still use reference works, they're just the works of fiction you want to emulate (or history books for historical settings, etc) instead of rulebooks.
If you don't trust the referee running your D&D game, why are you playing with them? The difference in trust required for an FKR game vs a D&D game is minimal at best. Again, that's what Session 0 is for, getting on the same page as each other.