So a more apt analogy would be if your sorcerer with the basket of spell components also claimed that he could cast as many spells as he wanted, as long as he had the material components.
Has the sorcerer player actually made this claim explicitly with respect to his cards, or are you just putting these words in his mouth? For my part, I certainly don't make this claim with my bard. There is nothing about substituting one spellcasting implement for another that implies the character should be able to cast more spells. I feel like you're forcing this point in order to make your parallel.
Now, as long as he just talks about it and doesn't actually *do* it (that is, he never exceeds the spellcasting that would be permitted by the rules, however he narrates it) then I'd be fine with it.
If a
hypothetical player made this claim, it would strain suspension of disbelief, because the obvious follow-up question to him not actually doing it is "Why not?" I'm not fine with narration that introduces plot holes or risk thereof. If the player's character concept calls for always-available magical power, he should go for a class the mechanics of which let him do that. If the player's character concept calls for him to know stuff, he should go for an ability score array the mechanics of which let him do that. Then he won't have to contrive narrative reasons why he can't do something. He'll be able to choose whether to do it or not, reacting to the situation in whatever way makes sense for the character.
The whole point of
having mechanics is to let your character do the stuff that his concept says he should. If you opt into a complete conceptual-mechanical mismatch, that's like trying to eat soup with a fork when
there's a spoon right there. Yeah, you may be able to kludge up some awkward approach, but it's still going to be a lot messier than the alternative, and don't expect us to be impressed by it.
According to what you and Max and Danny have written I would assume you would have a big problem with both of those examples, because once you allow the player to narrate it that way, what's to prevent him from actually demanding that he gets to cast more spells. Or, as I suggested before, what happens if he gets charmed by a Vampire who then orders him to keep casting until he's out of cards/components?
Yeah, pretty much. If I ask you to offer answers to these questions, no doubt you'll have some
ad hoc reasons why it doesn't work. But I prefer events in a story to unfold organically and according to a consistent internal logic, rather than things happening to serve some external need.