The term "relevant" might be an understatement here.
Layman’s guess: if there’s no generalizable proof describing why this works and the only method of proof is enunerating every case. That said, I kinda doubt that that is the case here, we probably just need a craft way of describing this so that we may come up with a crafty way of proving it :)
If there is a proof of no generalizable proof, that is interesting in and of itself. If there is not, then doesn't that mean we haven't found it yet (or proven it impossible, or proven it impossible to prove if impossible...). If we are still at the point of enumerating each case, that means our knowledge of the subject matter is lacking the deeper understanding to solve it in a nicer fashion.