Bedrockgames
I post in the voice of Christopher Walken
Well, at least in 5e it is trivially easy to make a fighter who is good at pick pocketing.
Certainly this is going to vary tremendously by edition and system. My point is just character creation usually leads to these kinds of limitations unless the system is extensively engineered.
As for the person who can only cast fireball and nothing else, I'd say that's like wanting to know calculus without knowing arithmetic; it's just not how that stuff works. Now magic being fiction, we of course can decide how it works, but personally I prefer if the rules and fiction are aligned. If every bloody PC class learns their spells level by level, having to go through lower ones first, then I kinda want to have the setting metaphysics to reflect that.
But this is your rationale. We can come up with any rationale we want here. If we took it to fighting, you don't generally learn a kick like spinning hook kick until you have mastered front kick, round house kick, back kick, etc. But I have no doubt I could teach my niece of nephew to just perform a spinning hook kick. Same goes for music even, which I think is probably little closer to vancian magic. It would be hard for me to just teach you stairway to heaven and no other songs along the way. But it could be done. I could even teach it to you, without teaching you any of the chords. You would be playing the chords as they are performed in the song, but I wouldn't necessarily have to have you know what chords you are playing and how to play them in different places on the guitar neck.
We don't know the exact ground level details of spell casting, and again these do vary buy edition, but I don't see why one must learn 1st level spells just to learn a third level one. Those limits are obviously based on power and balance considerations. You see this all the time in fantasy stories where someone who isn't particularly adept learns one powerful spell. Sure there may be principles she must learn to cast that third level spell, but that doesn't mean she needs to be a 5th level wizard with all that entails.
Ultimately this is subjective, but I think it is a heck of a lot more believable that a GM has the ability to say "this character was taught fireball by her protective but largely absent father" and still make her a zero level nobody. I may want to throw in something to reflect her poor command of spell casting overall (a chance of failure perhaps). But I think that matches what is going on in the setting with that character more than walking her through five levels of mage.
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