Actually this could be a nice service to offer now. We might worry that someday public key crypto will be broken, and we wouldn’t want all our old bank statements to become public at that point I guess.
Yes, it was inconvenient, but hardly an impossible thing to do. Banks manage to communicate the PIN for your card safely every time you open an account, I'm sure this could be done as well.
Also: my bank access is done entirely through an app that obscures its internal implementation. It could already be using OTP and it wouldn't make any difference to me, nor would I be able to tell(my point is that the user wouldn't need to keep a piece of paper that they would need to type in anywhere - the internal implementation of tools we use every day would change, but most users wouldn't even notice)