I had a revelation this year, I have a new bank acc and not familiar with their procedure. First few calls they did to me, they have asked some good questions, aside from my name thy were negative - e.g. did you do X thing in your app, when we both know that I did not. But then last time an operator called and asked my PII question (birthday, address etc.). I got triggered and said "eh, sorry, won't tell you because unsafe". And she went "oh, no problem then - I will auth you in the app". Lo and behold, immediately I got push from bank app with her name, phone number calling and some details. So they do have a perfectly 1)safe, 2)repeatably reliable, 3) and fast way to authenticate customers. They just ignore it mostly. I'm still simultaneously like them and is angry on them.
tl;dr - bank calling you can do auth digitally on phone, but don't do it and don't advertise it to clients.
PS: I'm in EU.