Considering that most people nowadays often find it hard to store and protect their cryptocurrencies, it's best to delegate the responsibility to a middleman. A bank of crypto would fit the bill nicely, as people would be able to secure their cryptocurrencies without ever having to follow the necessary precautions to prevent hacks or theft. As long as the bank of crypto is highly regulated by the government, then it'll be here to stay for a long time. Still though, not everyone will agree to this as it greatly defeats the whole purpose of crypto and Blockchain technology. The idea of a bank providing crypto services would only prove to be viable for newcomers into cryptocurrency. People who're experienced in crypto, wouldn't need this in the first place.
Nonetheless, do you think that a Bank of Crypto will happen anytime soon? If so, why?

We do not know how such a bank will be accepted by the community. Nowadays, if we consider the growth of the security problem, it can be useful but, I assure you, including myself, those who do not agree will not be less. Actually I have seen something like you are looking for. Check out
World Bit Bank. As I remember, they wanted to establish a decentralized system that provided us with the services offered by banks today. I have seen the project last year, and I am unaware of how they are going on right now.