This could happen one day when banks can no longer compete with Bitcoin because everyone uses it like they currently use fiat money. But as long as fiat money remains trusted by all governments around the world, it will continue to be used by everyone, even if everyone loves Bitcoin as much as they love money. Banks could take advantage of this opportunity to earn fees when people buy or exchange Bitcoin through their services. However, I still prefer to stick with certain exchanges if I only want to exchange Bitcoin for other assets like fiat money.
It's been 16 years and until now, not many people think about and want to use bitcoin as a currency to replace fiat. People have completely accepted and used bitcoin only as a form of investment to make profits, and I don't think this will change in the future. Everyone is excited about what bitcoin has become.
We don't have to wait until everyone is using bitcoin as currency and banks are accepting bitcoin. Banks will soon offer bitcoin deposits, simply because they will be able to make a profit from it. There is no reason why they should ignore this idea.