I don't get it. Isn't Bitcoin created to eliminate the presence of banks and make it peer to peer. That's why I think that it is quiet contradictory to bank in crypto. I don't think that that would happen because we can be a bank of our own money ourselves isn't it. You can make it very secure by purchasing cold wallet and store your private keys away from any digital devices. Also if we talk about the government then honestly I think that it can't be avoided if you envision it be adapted throughout the world.
It does not make sense but since when only things that make sense are the most popular or the only ones to exist? Look at fiat, to have a whole system based on a currency that can be printed at will is a bad idea no matter how you look at it and despite this all currencies around the world are fiat.
A bitcoin bank does not makes sense either but I can assure it will exist and I could venture to say that banks will store the coins for the majority of people around the world as most people are too lazy to learn how to secure their coins properly.