I think your interpretation of what makes a classic is well nigh ferpick. But...

I am not sure that a classic is infallible in its ability to move you - though this might depend upon what you mean by an appropriate 'context'. If I have no ability to appreciate either Chinese, or North Indian classical music, is my context wrong? Or is it that, not having been exposed to them whilst growing up, I have no sub-conscious recognition of the forms at all - there is no lock in my head for which those memes have the key? But if that is the case, then why cannot the same apply to Western classical music?

I think this discussion/debate/argument can go round and round and....