You can always check the balance of your Case Wallet at
https://dashboard.choosecase.com/. If you think about it, displaying balance on the device itself may not be desired by all users who prefer to keep that information private. Customer support mentioned to me that a new production run was planned for January 2016.
I'm not sure I follow your line of reasoning. If you have the device in your hand (and can bypass the fingerprint scanner) you have pretty much full control over the bitcoins in the wallet. It seems really odd to me you could transfer coins out of the wallet but no see how many there are. I'm having a hard time coming up with a scenario where I would be more concerned about someone being able to see how many bitcoins I had in a wallet than being able to transfer them all to their own account.
Checking via the website is an option IF you have a device on you with a separate network connection. As a standalone device isn't Case supposed to remove the dependency on having something else connected to the Internet?