Bank is not the only one that asks about personal information. What about exchangers, you have to give your data and still everyone uses them. I think is not the main point of Bitcoin bank like it's not centralization. I think Bitcoin bank could move Bitcoin related services to another level without bad influence on Bitcoin.
I do not find any necessity of having bitcoin bank as we are already dealing with bitcoin comfortably just with wallets hence there will be no need of having any centralized authority for our bitcoin related stuff.
If you will be needing some bank for the purpose of buying and selling bitcoins, that does not mean you are in need of bitcoin bank. Bitcoin bank must be completely different like it will be in forcing us back to go from decentralisation into centralization.