Why not? That is, why does your bank need all that information about you? I give bank my money for safekeeping and the bank provides convenient access to it. Reliable access can be done with different methods using a different degree of anonymity.

At least in the US, banks requiring all sorts of information do it not even as their own business choice -- they do it because government regulators insist that this data is collected because security, because terrorism, because money laundering, etc.