I am very sure that one day, traditional Bank will begin to accept Bitcoin as a legit medium of exchange, people need to be given freedom to deposit their BTC directly just like the regular money. I believe that this will come to pass when the major world powers officially recognizes and adopts Bitcoin, this will make a foundation for banks to stand up and integrate it into their financial system. I believe in Bitcoin .
Why would I store my Bitcoins with a centralized bank or use a third party to transact Bitcoins when I have decentralized access? Is this ever a smart move? The main purpose of creating Bitcoin is to create a decentralized financial system and a peer-to-peer transaction system that allows you to transact anywhere in the world without the help of a third party.
So why would anyone rely on a bank to use Bitcoin? I doubt that what you are saying will happen or that many people will use it. I think no sane Bitcoiner would want to rely on a bank to use Bitcoin. Because Bitcoin is much safer and easier to transact with than a bank.
This may happen in the future depending on the laws of different countries. I am waiting to see the impact.