Depending on regulation and international politics, this can eventually take place in the future. When global authority identify Bitcoin as a legal means of exchange, then banks will have to follow if they must stay relevant. Presently some banks view it more as just asset than money. Adoption will only grow if government provide obvious rules and users continue to request it during transactions.
Yes, you have made the right comment. I agree with your comment. Of course, it is right that when talking about this issue, one must keep one's head, if banks will accept deposits from Bitcoiners, it may take a long time and depend on international policies. However, if banks collectively accept Bitcoin deposits, then a legal rule for Bitcoin will be introduced worldwide. However, I think that although this can happen, I do not know clearly how quickly it is possible, but I would like to request everyone to clear this issue more nicely. Thank you for presenting this valuable comment.