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?
It is very possible but I know not one bank that accepts bitcoin as direct deposit from your bitcoin wallet to your savings account. Because there is no one bank that has bitcoin as an option of their account. It might happen in the future if bitcoin will be as widespread as fiat.
Future means next generation or next to next generation. First thing is banks will oppose this Bitcoin, and they will never support to this Bitcoin. If it becomes legal, then they will lose their business, and it's a big loss for banks. So takes some years to become legal and to convince banks again it will take a number of years totally how many years it will take no idea.