I regularly conduct transactions at the branch of my local bank wherein they ask me for no credentials whatsoever. I also once forgot to bring my account number with me and the teller said "no worries, I'll look it up for you." Kind of horrifying.
That's scary. I wonder if incompetence like that could lead to a lawsuit in the case of a breach.
At this point I wouldn't be surprised if there exists a system that just asks for username with a checkbox "check here if you are the owner of this account"