> maintaining those tests when you don't have access to a platform with, say, 18-bit integers to test those tests, seems like it will end up with flawed tests.

No? I don't over generalize for features I don't use. I test to confirm the presence of the assumptions that I depend on. I want my code to fail to compile if my assumptions don't hold.

I don't recall if I verify CHAR_BIT or not but it wouldn't surprise me if I did.