Anonymity is the major reason why many prefer Bitcoin. Maintaining it in the e-Wallet is completely anonymous. For instance, depositing and withdrawing through Bitcoin eWallet is anonymous on its own, but in a really great Bitcoin casino, the process of signing up also is completely anonymous. Sites with features like these are the ones that attract many players. Cause gambling is still illegal at some countries, so this is the best feature to free gambling.
I am not sure why people want to stay anonymous while gambling. It is safe to stay low profile but honestly, not a lot of people are interested in guys like me. They won't even care if I roam around openly. Therefore, it is better to keep the bitcoin in wallets and wait for the price increments. Bitcoin is the future currency and it will be the most expensive asset also so I suggest not risking it in any way.
Don't you really know why it's important to be at least partially anonymous when gambling? Many people see it as an addiction or some other type of flaw, so players don't want to openly admit that they're gamblers. You won't see it under "interests" in any resume. People sometimes want to hide that they're gambling from members of their family and sometimes those people have access to their bank accounts.