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

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.