I disagree.
Bitcoin "bank" implies centralization in my view. Centralization implies single-point of failure which implies regulation etc etc etc.
Bitcoin enables you to be your own central bank and to protect your own net worth without it being someone else's counter-party risk.
The problem is that some people can't be bothered to protect their own wallet and want someone else to do it, for those people the idea of a bank may be a better idea, the solution is not that their should be a bank but how can we design one that isn't evil
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What a shame huh? People can't be fucked doing the minimum required to take responsibility for their own interests. Naturally there will be greedy operators willing to exploit their laziness. Bitcoin makes banks redundant and that is good. You can never underestimate the value of decentralization. Going back to a new central service every time a little invonvinience crops up is foolish and lazy. Let them try to create bitcoin banks though; let them try to invoke primitive technology as innovative solutions. People will get burned for no good reason, other than their own laziness.
Nobody said a fool and their bitcoin could never be parted. Any kind of central authority/service is the wrong kind of solution because it tries solving the wrong problem. Better that we have education facilities and tools that make security more intuitive while helping people to understand the need to take responsiblity in free-speech, democracy, safe sex, recycling/environment and yes, personal security (including by trying mitigate the risks borne of using centralised services to defer our responsibility.)
In summary, the market you have identified, is not in banking, but rather in security tools and education.