One day banks will accept Bitcoin as medium of exchange and accept deposits from bitcoiners. As soon as the world powers accept it as medium of exchange.
Banks hate Bitcoin. They don't accept it despite global acceptance. Besides, why use a bank when we can deposit it into our controlled wallet? Why give them a complicated job when we can do it personally? We don't need them. We do it on our own. That is one advantage of having this in place, where we have the fullest control and no need to spend money on others to guard our assets.
In fact, that is why banks dislike Bitcoin, as it will affect their income. So we don't expect them to welcome Bitcoin but rather push it away.
I say the same thing, if we can store our Bitcoin in a secure, controlled wallet, why would we use a bank? We don't need to use a bank at all, and especially Bitcoin never supports a third party, so we don't have to worry about whether the bank will accept it or not. We will keep our Bitcoin in our own wallet, we will operate with our own independence, we will not be dependent on others. Imagine if you want to transfer millions of dollars from one place to another in an instant, it is possible, but when you go to transact with a bank, they will not let you transfer millions of dollars, and even if they do, you have to abide by their rules. You have to be firm in their decision. If you are not firm in their decision, you will not work. So we are not worried at all about whether the bank will accept Bitcoin or not because we are very good with Bitcoin.
As people's interest in Bitcoin increases and the number of investors also increases, banks will definitely try to find ways to use these people for profit. There will have a time when banks can start storing Bitcoin. Especially in the case of global transactions. The work that banks are currently is done through fiat and they are profiting from that. In the future, they will try to profit by using Bitcoin. If banks get permission from the government to use Bitcoin, they will try their best to quickly adopt it in their systems.