I'm not sure that's the more general proposition. For me, that's become specific in a way that misses the focus of what I'm trying to get at in this discussion.
To put the above back into the OP's original context, class A is 'fighter', enumerated ability B is (say) the 'Healing Word' spell, and class C is 'Cleric'. If the player of the fighter asks "Can I cast 'Healing Word'?", my answer is no, they can't; but that's not really how I view the topic here.
Ultimately, I'm not trying to allow character build options, etc, to be duplicated, I'm trying adjudicate actions declared by my players. And I will absolutely think about those actions within the context of existing mechanics, niche protection, and table fairness as you note below. I guess this point might seem like semantics, but if I'm not trying to duplicate a mechanic, but instead frame the next roll, that opens up scope of both success and failure outcomes.
I don't disagree with you; instead, I think that the issue is actually different than the one diagnosed. I had another take on it in this thread-

D&D 5E - Context Switching Paralysis, or Why we Will Always Have the Thief Debate
Among a certain group of people, there is a driven need to use a mocking term (we'll call it "MMI") to refer to playing D&D and other types of games. However, while the specific pejorative term may have been coined in 2005, the actual debate and the issues it illuminates goes back much farther...

For me, this is more of an interstitial issue. When a game is considered "complete" or "rule-bound" (everything must be done according to rule), the answer is trivial. That which is not permitted, is denied.
On the other hand, games that do not depend on rules have a different approach entirely. It's also a trivial issue.
The hard cases tend to be games that have a mix of rules and "not-rules" like D&D. Here, how do the enumerated rules constrain the not-rules? I don't think it's an issue about semantics at all- it's fundamental to games, like D&D (esp. 5e and TSR-era D&D) that tend to have both highly codified rules (combat, spells) and also a high allowance for not-rules or rulings.
The more rules you have, the more you have to consider the rules when you are making decisions about the not-rules.