A bank for bitcoins obviously does not make sense, since the blockchain is already a bank in itself.
But it is clear that there will always be a need for banking services: intermediation, leasing, advances, credits, investments, etc.
So surely the banks will create specific offers for the crypto sector.
Other than what you have said, I would like to add the fact that most people don't really care or understand this stuff. It's sad to see a lot of people not trusting themselves when it comes to technology. It's like they are afraid of it yet they always have an iPhone on their hands. iPhone's user interface is quite simple so those who don't like tech tend to avoid using an Android phone. They buy iPhones instead and while it's a really bad phone to buy with that amount of money, they get to look rich with it because it's expensive.
With that being said, a lot of people wouldn't be trusting themselves with something like crypto. Money is involved and they sure would want somebody else to hold it for them. This is where the banks would enter the scene. People would think that it's unhackable since it's in a bank but I think it really is bad to put your money in something centralized as they can be the perfect target for hackers. Nonetheless, I just hope that these people would know that the banks would not guarantee money back when they got a security breach because this is not like fiat currency which they can just print 24/7. Once your bitcoins are gone, be it your fault or the bank's fault, they are already gone. I hope they would know that at least.
