Is it possible that banks would accept bitcoin as your deposits directly from your bitcoin wallet? Or they will ban it because of internet security reasons?
I don't know why you would want to do that. First it wouldn't be a deposit, it would be just an exchange so if payments are accepted in bitcoin, you don't really need to exchange them for fiat. If you want to exchange them for fiat, then using an exchange or services like neteller, payza, and who knows paypal, will be more than enough I guess. For bitcoins to be deposit in banks, then they would have to create a wallet themselves, and I don't see any advantages in that.