In Europe we have the PSD2 open banking [1] directive which essentially gives developers a standard api access to banking operations on behalf of a user.
It is a requirement for banks to implement this and the FSA will be on your neck if you are not compliant with the standard.
To access that API you need a license as an authorised third-party provider (TPP), don't you? So in practice it is only for businesses capable of pushing through the bureaucracy.