I think you have correctly identified an implausible claim! Of course, most languages aren't written at all ... or at least don't have a traditional written fo

I think you have correctly identified an implausible claim! Of course, most languages aren't written at all ... or at least don't have a traditional written form that is sufficiently well established for someone to say that the "language" has case rather than a particular (proposed) way of writing it. However, I rather suspect that the majority of languages in which books are published use some variant of the Latin alphabet and do, therefore, have case. (The only language I've heard of that uses the Latin alphabet without case is Lojban!) On the other hand, if you weight languages by the number of (native) speakers, since about three quarters of the world's population lives in China, India, Pakistan, Bangladesh, Japan or Korea, probably it's true that most people don't use case in their main language.