I’d do a reset in the “wrong case” to see if it does any harm before selling your spare. Of course if it does fail that proves the case is tied to the buds and so making it useless to sell!
I cannot see any valid technical reason why a case is tied to the buds. That would be bizarre, cause huge manufacturing costs. Imagine in the factory when they test the L and R and case and say the case fails, they’d have to discard the L and R buds also. Illogical therefore on cost grounds. And no technical benefit of tying them together. I can see technical reasons why a L and R bud are tied to each other as that helps stop them getting confused.
The perfect design I’d like is none of the parts are tied to each other, and all the reset signal does is then tie whichever L and R are in the case at the same time so you can buy separately each part. That is a more complex process.