I would expect the full chaincases to have chains, not belt drive. The bikes I've seen with chaincases all have chains (hence the name); since the belt can't be broken and relinked like a chain, it wouldn't fit into many full chain cases.

I wouldn't expect daily commuters in Europe or Japan to use belt drive - there are lots of cheap reliable bicycles with chains available used and new that can't accept belt drive, so they would have to actively look for an unusual (belt) bicycle that would be harder to have serviced.