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?
Well there are some banks who are allowing Bitcoin trade and accepting it, but not all will do one of the main reasons they won't accept is cause they can't risk being unlisted cause Bitcoin is not accepted as a legal currency. Even if your bank starts accepting it be careful if they are authorised, cause there are hardly any bank that can accept it.
Name me one Bank that takes bitcoins. It seems to me that at this time banks do not. The maximum that banks can be the intermediary between you and the exchanger you are changing the bitcoins to Fiat. Banks will never get a license to use bitcoins.