Banks should be insured; I don't know if that's possible for a crypto-bank without a lot of work/lengthy legal process.
In order for a crypto bank to be insured, they would have to have very tight security and monitoring tools. The insurance company will want to make sure the funds aren't stolen by the most likely source -
internal.
Bank? Sometimes the definition and the interpretation that is given to bank makes it seems something easy and all about money. Having a bank goes beyond the money part. Even in the fiat world with a lot or model to learn from, industry experts to kick things running, already functioning software both for security and operations, an established connectivity to the network grid in a short period of time, its still not a child's play because of the amount of effort needed not to talk of bitcoin bank where all of those factors listed are practically nonexistent.
Personally, I won't keep my coins in a "bitcoin bank" not because of it will scam but because of two things
1. I can't bring myself to trust someone with my money, and someone so far away to decide what to do with it and when to assess it.
2. The idea of "bitcoin bank" itself negates the bitcoin itself as part of it is giving one absolute control over his resources and banks are known to not be fully aligned with that simple objective.
Those 2 keypoints are exactly why bitcoin bank wont really be an effective idea not only having lots of factors and considerations but also i dont think people would really use such service since we do know the main purpose why bitcoin is being created on the very first place which is on having the full control of our funds which means why create banks if we can able to make ourselves our own banks.
Trusting out other services acts as a storage of our bitcoin holdings is already being done by most wallets existing on the net.