They are contrast against each other. Banks are centralized because they complying with the rules of the government. Bitcoin is decentralise. Means it's not complied with the policy given by the government. That's why i don't think it will happen. Besides, Bitcoin is a bank itself. Just choose your desired wallet and keep it as long as you want.
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?
Yes it is possible. Many banks today are accepting bitcoins. I can say that the banks will support the bitcoin.
Really? What bank? I never heard about it before.
I only know Ripple(XRP). Ripple is used by many banks. They said it is a decentralized platform. But i doubt about that.